1 Foundations 2 Solving Linear Equations 3 Graphs And Functions 4 Systems Of Linear Equations 5 Polynomials And Polynomial Functions 6 Factoring 7 Rational Expressions And Functions 8 Roots And Radicals 9 Quadratic Equations And Functions 10 Exponential And Logarithmic Functions 11 Conics 12 Sequences, Series And Binomial Theorem Chapter9: Quadratic Equations And Functions
9.1 Solve Quadratic Equations Using The Square Root Property 9.2 Solve Quadratic Equations By Completing The Square 9.3 Solve Quadratic Equations Using The Quadratic Formula 9.4 Solve Quadratic Equations In Quadratic Form 9.5 Solve Applications Of Quadratic Equations 9.6 Graph Quadratic Functions Using Properties 9.7 Graph Quadratic Functions Using Transformations 9.8 Solve Quadratic Inequalities Chapter Questions Section: Chapter Questions
Problem 395RE: In the following exercises, solve using the Square Root Property. 395. y2=144 Problem 396RE: In the following exercises, solve using the Square Root Property. 396. n280=0 Problem 397RE: In the following exercises, solve using the Square Root Property. 397. 4a2=100 Problem 398RE: In the following exercises, solve using the Square Root Property. 398. 2b2=72 Problem 399RE: In the following exercises, solve using the Square Root Property. 399. r2+32=0 Problem 400RE: In the following exercises, solve using the Square Root Property. 400. t2+18=0 Problem 401RE: In the following exercises, solve using the Square Root Property. 401. 23w220=30 Problem 402RE: In the following exercises, solve using the Square Root Property. 402. 11.5c2+3=19 Problem 403RE: In the following exercises, solve using the Square Root Property. 403. (p5)2+3=19 Problem 404RE: In the following exercises, solve using the Square Root Property. 404. (u+1)2=45 Problem 405RE: In the following exercises, solve using the Square Root Property. 405. (x14)2=316 Problem 406RE: In the following exercises, solve using the Square Root Property. 406. (y23)2=29 Problem 407RE: In the following exercises, solve using the Square Root Property. 407. (n4)250=150 Problem 408RE: In the following exercises, solve using the Square Root Property. 408. (4c1)2=18 Problem 409RE: In the following exercises, solve using the Square Root Property. 409. n2+10n+25=12 Problem 410RE: In the following exercises, solve using the Square Root Property. 410. 64a2+48a+9=81 Problem 411RE: In the following exercises, complete the square to make a perfect square trinomial. Then write the... Problem 412RE: In the following exercises, complete the square to make a perfect square trinomial. Then write the... Problem 413RE: In the following exercises, complete the square to make a perfect square trinomial. Then write the... Problem 414RE: In the following exercises, complete the square to make a perfect square trinomial. Then write the... Problem 415RE: In the following exercises, solve by completing the square. 415. d2+14d=13 Problem 416RE: In the following exercises, solve by completing the square. 416. y26y=36 Problem 417RE: In the following exercises, solve by completing the square. 417. m2+6m=109 Problem 418RE: In the following exercises, solve by completing the square. 418. t212t=40 Problem 419RE: In the following exercises, solve by completing the square. 419. v214v=31 Problem 420RE: In the following exercises, solve by completing the square. 420. w220w=100 Problem 421RE: In the following exercises, solve by completing the square. 421. m2+10m4=13 Problem 422RE: In the following exercises, solve by completing the square. 422. n26n+11=34 Problem 423RE: In the following exercises, solve by completing the square. 423. a2=3a+8 Problem 424RE: In the following exercises, solve by completing the square. 424. b2=11b5 Problem 425RE: In the following exercises, solve by completing the square. 425. (u+8)(u+4)=14 Problem 426RE: In the following exercises, solve by completing the square. 426. (z10)(z+2)=28 Problem 427RE: In the following exercises, solve by completing the square. 427. 3p218p+15=15 Problem 428RE: In the following exercises, solve by completing the square. 428. 5q2+70q+20=0 Problem 429RE: In the following exercises, solve by completing the square. 429. 4y26y=4 Problem 430RE: In the following exercises, solve by completing the square. 430. 2x2+2x=4 Problem 431RE: In the following exercises, solve by completing the square. 431. 3c2+2c=9 Problem 432RE: In the following exercises, solve by completing the square. 432. 4d22d=8 Problem 433RE: In the following exercises, solve by completing the square. 433. 2x2+6x=5 Problem 434RE: In the following exercises, solve by completing the square. 434. 2x2+4x=5 Problem 435RE: In the following exercises, solve by using the Quadratic Formula. 435. 4x25x+1=0 Problem 436RE: In the following exercises, solve by using the Quadratic Formula. 436. 7y2+4y3=0 Problem 437RE: ]In the following exercises, solve by using the Quadratic Formula. 437. r 2 r42=0 Problem 438RE: In the following exercises, solve by using the Quadratic Formula. 438. t2+13t+22=0 Problem 439RE: In the following exercises, solve by using the Quadratic Formula. 439. 4v2+v5=0 Problem 440RE: In the following exercises, solve by using the Quadratic Formula. 440. 2w2+9w+2=0 Problem 441RE: In the following exercises, solve by using the Quadratic Formula. 441. 3m2+8m+2=0 Problem 442RE: In the following exercises, solve by using the Quadratic Formula. 442. 5n2+2n1=0 Problem 443RE: In the following exercises, solve by using the Quadratic Formula. 443. 6a25a+2=0 Problem 444RE: In the following exercises, solve by using the Quadratic Formula. 444. 4b2b+8=0 Problem 445RE: In the following exercises, solve by using the Quadratic Formula. 445. u(u10)+3=0 Problem 446RE: In the following exercises, solve by using the Quadratic Formula. 446. 5z(z2)=3 Problem 447RE: In the following exercises, solve by using the Quadratic Formula. 447. 18p215p=120 Problem 448RE: In the following exercises, solve by using the Quadratic Formula. 448. 25q2+310q=110 Problem 449RE: In the following exercises, solve by using the Quadratic Formula. 449. 4c2+4c+1=0 Problem 450RE: In the following exercises, solve by using the Quadratic Formula. 450. 9d212d=4 Problem 451RE: In the following exercises, determine the number of solutions for each quadratic equation. 451. (a)... Problem 452RE: In the following exercises, determine the number of solutions for each quadratic equation. 452. (a)... Problem 453RE: In the following exercises, identify the most appropriate method (Factoring, Square Root, or... Problem 454RE: In the following exercises, identify the most appropriate method (Factoring, Square Root, or... Problem 455RE: In the following exercises, solve. 455. x414x2+24=0 Problem 456RE: In the following exercises, solve. 456. x4+4x232=0 Problem 457RE: In the following exercises, solve. 457. 4x45x2+1=0 Problem 458RE: In the following exercises, solve. 458. (2y+3)2+3(2y+3)28=0 Problem 459RE: In the following exercises, solve. 459. x+3x28=0 Problem 460RE: In the following exercises, solve. 460. 6x+5x6=0 Problem 461RE: In the following exercises, solve. 461. x2310x13+24=0 Problem 462RE: In the following exercises, solve. 462. x+7x12+6=0 Problem 463RE: In the following exercises, solve. 463. 8x22x13=0 Problem 464RE: In the following exercises, solve by using the method of factoring, the square root principle, or... Problem 465RE: In the following exercises, solve by using the method of factoring, the square root principle, or... Problem 466RE: In the following exercises, solve by using the method of factoring, the square root principle, or... Problem 467RE: In the following exercises, solve by using the method of factoring, the square root principle, or... Problem 468RE: In the following exercises, solve by using the method of factoring, the square root principle, or... Problem 469RE: In the following exercises, solve by using the method of factoring, the square root principle, or... Problem 470RE: In the following exercises, solve by using the method of factoring, the square root principle, or... Problem 471RE: In the following exercises, solve by using the method of factoring, the square root principle, or... Problem 472RE: In the following exercises, solve by using the method of factoring, the square root principle, or... Problem 473RE: In the following exercises, solve by using the method of factoring, the square root principle, or... Problem 474RE: In the following exercises, solve by using the method of factoring, the square root principle, or... Problem 475RE: In the following exercises, solve by using the method of factoring, the square root principle, or... Problem 476RE: In the following exercises, graph by plotting plot. 476. Graph y=x22 Problem 477RE: In the following exercises, graph by plotting plot. 477. Graph y=x2+3 Problem 478RE: In the following exercises, determine if the following parabolas open up or down. 478. a. y=3x2+3x1... Problem 479RE: In the following exercises, determine if the following parabolas open up or down. 479. a. y=x2+8x1... Problem 480RE: In the following exercises, find ? the equation of the axis of symmetry and ? the vertex. 480.... Problem 481RE: In the following exercises, find ? the equation of the axis of symmetry and ? the vertex. 481.... Problem 482RE: In the following exercises, find the x- and y-intercepts. 482. y=x24x+5 Problem 483RE: In the following exercises, find the x- and y-intercepts. 483.y=x28x+15 Problem 484RE: In the following exercises, find the x- and y-intercepts. 484. y=x24x+10 Problem 485RE: In the following exercises, find the x- and y-intercepts. 485. y=5x230x46 Problem 486RE: In the following exercises, find the x- and y-intercepts. 486. y=16x28x+1 Problem 487RE: In the following exercises, find the x- and y-intercepts. 487. y=x2+16x+64 Problem 488RE: In the following exercises, graph by using its properties. 488. y=x2+8x+15 Problem 489RE: In the following exercises, graph by using its properties. 489. y=x22x3 Problem 490RE: In the following exercises, graph by using its properties. 490. y=x2+8x16 Problem 491RE: In the following exercises, graph by using its properties. 491. y=4x24x+1 Problem 492RE: In the following exercises, graph by using its properties. 492. y=x2+6x+13 Problem 493RE: In the following exercises, graph by using its properties. 493. y=2x28x12 Problem 494RE: In the following exercises, find the minimum or maximum value. 494. y=7x2+14x+6 Problem 495RE: In the following exercises, find the minimum or maximum value. 495. y=3x2+1210 Problem 496RE: In the following exercises, solve. Rounding answers to the nearest tenth. 496. A ball is thrown... Problem 497RE: ??In the following exercises, solve. Rounding answers to the nearest tenth. 497. A daycare facility... Problem 498RE: In the following exercises, graph each function using a vertical shift. 498. g(x)=x2+4 Problem 499RE: In the following exercises, graph each function using a vertical shift. 499. h(x)=x23 Problem 500RE: In the following exercises, graph each function using a vertical shift. 500. f(x)=(x+1)2 Problem 501RE: In the following exercises, graph each function using a horizontal shift. 501. g(x)=(x3)2 Problem 502RE: In the following exercises, graph each function using a horizontal shift. 502. f(x)=(x+2)2+3 Problem 503RE: In the following exercises, graph each function using a horizontal shift. 503. f(x)=(x+3)22 Problem 504RE: In the following exercises, graph each function using a horizontal shift. 504. f(x)=(x1)2+4 Problem 505RE: In the following exercises, graph each function using a horizontal shift. 505. f(x)=(x4)23 Problem 506RE: In the following exercises, graph each function. 506. f(x)=2x2 Problem 507RE: In the following exercises, graph each function. 507. f(x)=x2 Problem 508RE: In the following exercises, graph each function. 508. f(x)=12x2 Problem 509RE: In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the... Problem 510RE: In the following exercises, rewrite each function in the f(x)=a(xh)2+k form by completing the... Problem 511RE: In the following, (a) rewrite each function in f(x)=a(xh)2+k form and (b) graph it by using... Problem 512RE: In the following, (a) rewrite each function in f(x)=a(xh)2+k form and (b) graph it by using... Problem 513RE: In the following, (a) rewrite each function in f(x)=a(xh)2+k form and (b) graph it by using... Problem 514RE: In the following, (a) rewrite each function in f(x)=a(xh)2+k form and (b) graph it by using... Problem 515RE: In the following, (a) rewrite each function in f(x)=a(xh)2+k form and (b) graph it by using... Problem 516RE: In the following, (a) rewrite each function in f(x)=a(xh)2+k form and (b) graph it by using... Problem 517RE: In the following exercises, write the quadratic function in f(x)=a(xh)2+k form. Problem 518RE: In the following exercises, write the quadratic function in f(x)=a(xh)2+k form. Problem 519RE: In the following exercises, solve graphically and write the solution in interval notation. 519.... Problem 520RE: In the following exercises, solve graphically and write the solution in interval notation. 520.... Problem 521RE: In the following exercises, solve graphically and write the solution in interval notation. 521.... Problem 522RE: In the following exercises, solve graphically and write the solution in interval notation. 522.... Problem 523RE: In the following exercises, solve graphically and write the solution in interval notation. 523.... Problem 524RE: In the following exercises, solve graphically and write the solution in interval notation. 524.... Problem 525RE: In the following exercises, solve graphically and write the solution in interval notation. 525.... Problem 526RE: In the following exercises, solve graphically and write the solution in interval notation. 526.... Problem 527RE: In the following exercises, solve graphically and write the solution in interval notation. 527.... Problem 528RE: In the following exercises, solve graphically and write the solution in interval notation. 528.... Problem 529PT: Use the Square Root Property to solve the quadratic equation 3(w+5)2=27. Problem 530PT: Use Completing the Square to solve the quadratic equation a28a+7=23. Problem 531PT: Use the Quadratic Formula to solve the quadratic equation 2m25m+3=0 . Problem 532PT: Solve the following quadratic equations. Use any method. 532. 2x(3x2)1=0 Problem 533PT: Solve the following quadratic equations. Use any method. 533. 94y23y+1=0 Problem 534PT: Use the discriminant to determine the number and type of solutions of each quadratic equation. 534.... Problem 535PT: Use the discriminant to determine the number and type of solutions of each quadratic equation. 535.... Problem 536PT: Solve each equation. 536. 4x417x2+4=0 Problem 537PT: Solve each equation. 537. y23+2y133=0 Problem 538PT: For each parabola, find (a) which direction it opens, (b) the equation of the axis of symmetry, (c)... Problem 539PT: For each parabola, find (a) which direction it opens, (b) the equation of the axis of symmetry, (c)... Problem 540PT: Graph each quadratic function intercepts, the vertex, and the equation of the axis of symmetry. 540.... Problem 541PT: Graph each quadratic function intercepts, the vertex, and the equation of the axis of symmetry. 541.... Problem 542PT: In the following exercises, graph each function using transformations. 542. f(x)=(x+3)2+2 Problem 543PT: In the following exercises, graph each function using transformations. 543. f(x)=x24x1 Problem 544PT: In the following exercises, solve reach inequality algebraically and write any solution in interval... Problem 545PT: In the following exercises, solve reach inequality algebraically and write any solution in interval... Problem 546PT: Model the situation with a quadratic equation and solve by any method. 546. Find two consecutive... Problem 547PT: Model the situation with a quadratic equation and solve by any method. 547. The length of a diagonal... Problem 548PT: Model the situation with a quadratic equation and solve by any method. 548. A water balloon is... Problem 546PT: Model the situation with a quadratic equation and solve by any method. 546. Find two consecutive...
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Solve the equation by using the quadratic formula . (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)
(a) Give real answers exactly.
x =
(b) Give real answers rounded to two decimal places.
x =
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
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