How can I find a quadratic equation, that's in standard form, with a, b, and c all in terms of a? And I only have two points, (1,1) and (3,7). According to my teacher, my equation should still have the parabola pass through those two points no matter what value a is.

Q: Form a quadratic equation with roots 1/5 and −2 with integer coeffecients.

A: 15 & -2.

Q: Based on data from the U.S. Bureau of Public Roads, a model for the total stopping distance of a…

A: Find ds/dv using first derivative and exponent rule of derivative.

Q: Discuss the nature of the quadratic form x2+4xy+6xz-y2+2yz+4z2

A:

Q: find the quadratic function for which:   Vertex is 1 - 1, 22; contains the point 11, 62

A: Vertex form of a quadratic function: y=ax-h2+k        ...(1) Where (h, k) is the vertex.

Q: My neighbor and I like to kick a soccer ball back and forth to each other over the fence. If we each…

A: Consider the given scenario. Given that the neighbour's location in the picture is given by the…

Q: Show that the product of the roots of a quadratic equation is c/a .

A: Consider the quadratic equation ax2+bx+c=0 Also consider that α and β are the roots of the quadratic…

Q: A farmer wishes to enclose his armadillos into a rectangular region that will be bounded on one side…

A:

Q: 5. Write the equation of a parabola that takes a maximum value of 4 at r = -2.

A: We need to find equation of parabola.

Q: Find the equation of the parabola given 3 points using quadratic formula. (33,-9) (49,23) (68,3)

A: We have to find the equation of the parabola given 3 points using the quadratic formula. The three…

Q: In 1993​, the sports league introduced a salary cap that limits the amount of money spent on​…

A:

Q: What is the largest value of the quadratic form 5x} – 3x; if x'x = 1?

A:

Q: What is the solution to this quadratic, -3x2 + 8x - 6 = 0 -4 +iv21 3 4±iv2 -4 2iv2 4 +iv2 {*}

A:

Q: True or False If the discriminant of a quadratic equationis positive, then the equation has two…

A: Solution of an equation f(x)=0 is the value of x which when substituted in the equation satisfies…

Q: Find the equation of the parabola given 3 points using quadratic formula. (-3,38) (25,51) (-1,65)

A:

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=9−x2…

A:

Q: Consider the following quadratics: Q1:x2+y2-5z2-9=0 Q2:x2+y2-8z2=0 Calculate the distance of the set…

A: Given Q1:x2+y2-5z2-9=0Q2:x2+y2-8z2=0

Q: # 3) Create the equation of the cubic, in standard form, that has x-intercepts of 3, -1, and 2…

A:

Q: Find the roots of 2x quadratic equation - 2/x2 +1 = 0,if they exist using the

A: Given equation is 2x2-22x+1=0 find the roots of the quadratic equation

Q: Find the quadratic equation through the origin that is a best fit for the points: (1,1), (2,5),…

A:

Q: How can I write a quadratic equation when I am given the vertex and another point of the graph?

A: Definition used -                    The vertex form of quadratic equation is given by -…

Q: Find the quadratic equation whose roots are (3-j5) and (2 + j4).

A:

Q: What is the equation of a quadratic in standard form, given the zeros x = 3 and x = 6 and the point…

A: The solution is given below.

Q: Compute the value of the discriminant and give the number of real solutions of the quadratic…

A: Suppose ax2+bx+c = 0 is a quadratic equation. The discriminant of the quadratic equation is b2-4ac.…

Q: Find two quadratic functions, one that opens upward and one that opens downward , whose graphs have…

A:

Q: Determine the equation of the quadratic with roots of of -32. +13 -2± √2 and that has a y-intercept

A:

Q: Show that the cubic equation 2x3−3x2−15=0 has a solution in the interval (2,3).

A: Cubic Equation: Let f(x)=2x3-3x2-15We need find that there is a solution between (2,3)

Q: Show that the sum of the roots of a quadratic equation is - b/a

A: To show that the sum of the roots of a quadratic equation is -ba.

Q: Which of the following quadratic equations contains the vertex (-5, 6) and has a y-intercept of (0,…

A: Given: - The vertex of the quadratic equation is, (-5,6) and has a y-intercept of (0,31) To find: -…

Q: A parabola has its turning point at x = -4 and one of the x-intercepts is x = -3. What is the x…

A: Given Data: The x coordinates of the turning point of the parabola is: x=-4 One of the x-intercepts…

Q: If the discriminant of a quadratic equation is 0, then the equation has

A:

Q: What is the equation of a quadratic function y = f(x) with two irrational zeros,-h and h where h is…

A: Given,         The equation of a quadratic function y=fx with two irrational zeros, -h          and…

Q: what are the steps to solve an equation of quadratic type:2X+9√X=5

A: Given,

Q: Show that in general, the sum of the roots of a quadratic equation ax² + bx + c = 0 is whereas the…

A: We have to solve given problem:

Q: 10 -10 -5 10 -5 -10

A: If the graph of the quadratic function crosses the x-axis at two points then we have two solutions.…

Q: Do you wholly agree with the statement that “the domain and range of a quadratic equation will be…

A: The quadratic function is of form  f(x) =ax2+bx+c the graph of a quadratic function F(x) is called…

Q: In 1993​, the sports league introduced a salary cap that limits the amount of money spent on​…

A:

Q: Find the intercepts of the graph of each quadratic function. Show solutions also. 1. y = 4x^2+8x+3…

A: 1. y=4x2+8x+3 Y intercept is where x=0. So, y=4×02+8×0+3=3 So, y  intercept is (0,3)      x…

Q: quadratic

A:

Q: Compute the value of the discriminant and give the number of real solutions of the quadratic…

A: Consider the given quadratic equation. 3x2-8x+2=0 The objective of the question is to find the…

Q: Find the nature of the quadratic form 2x2+2y2+2z2+2yz

A:

Q: 6. Determine the equation of the quadratics with x-intercepts of 2 and -2 and a y- intercept of-6.

A:

Q: (4) Show that in general, the sum of the roots of a quadratic equation ax² + bx + c = 0 b is whereas…

A:

Q: Compute the ralue of the discriminant and give the number of realSolutions of the quadratic…

A: we have to find the discriminant and the number of real solutions

Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

A: The rectangle has its base on the x-axis and its other two vertices above the x-axis and lying on…

Q: If the discriminant of a quadratic equation is 2, then the equation has

A: The discriminant of a quadratic equation is given by b2-4ac We know that when the b2-4ac>0 then…

Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

A:

Q: (4) Show that in general, the sum of the roots of a quadratic equation ax? + bx + c = 0 b is whereas…

A:

Q: Find the equation, in vertex form, of the quadratic equation with zeros -1 and 7 and through the…

A: Given: The roots of the quadratic equation as -1 and 7 and the graph of quadratic equation is…

Q: Find the quadratic function for which: Contains the points (0, 5), (1, 2), and (3, 2)

A: The given points are,  (0, 5), (1, 2), and (3, 2). The quadratic equation is of the form y=ax2+bx+c.…

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.