In Exploration 2.2.1, you graphed a quadratic function with complex roots. When you graphed this quadratic and its complex parabola, what was the relationship between the parabola in the real plane and the parabola in the complex plane? They opened in opposite directions and were parallel to one another. They opened in opposite directions and were perpendicular to one another. They opened in same direction and were parallel to one another. They opened in same direction and were perpendicular to one another.

Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function : f(x) =…

A: Here given an equation of the parabola

Q: If the roots of x²-ax+b=0 is twice the other.find b in terms of a

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Q: The vertex of a parabola is located at (−5, 6). If the parabola has a y-intercept of (0, 231), which…

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Q: Find the vertex of the parabola. f(x) = 2x + 16x + 39 (х, у) %3

A: We have to find vertex

Q: Find the equation of the parabola whose axis is parallel to the x-axis and passes through the points…

A: We will find out the required value.

Q: Ex) Algebraically find the roots of the quadratic: rC) =}cx - 29° - 6

A: Given equation is; f(x)=12(x-2)2-6 Put f(x)=0x2+4-4x2-6=0x2-4x+4=12x2-4x-8=0

Q: Can you please solve for 5A + 5B

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Q: ,2 The vertex of the parabola of f(x)=x²+x is

A: Equation of the parabola :y=a(x-h)2+kwhere (h,k) = vertex of the parabola

Q: Let x₁, x₂ are the roots of the quadratic equation x² + ax + b = 0, where a, b are complex numbers…

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Q: You are given a quadratic equation of the form (x – p)(x – q) = 0. Show that the axis of symmetry of…

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Q: Write the equation of the parabola that has the same shape as f(x) = 3x² but with vertex (7,6) in…

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Q: QUESTION 7 Select all the complex solutions for 4x2 + 3x+7=0. O A. -3+i/103 8 O B. -3-iv19 4 OC.…

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Q: Identify the x-intercept(s) of this parabola. 10 8- 6- 4- -6 -2 2. 6 -4 O (3. 0)

A: x-intercept is the point where the graph crosses the x-axis.

Q: Please confirm if the selected answer is correct ?

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Q: Find an equation for the hyperbola whose graph is below. -1412-10-8 -61-4 -25 4,6 8 1012|14 CO

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Q: The vertex of the parabola f(x) = – 2(x+2) - 3, is O a. (2, 3) Ob.(-2, -3) OC (2, -3) O d. (-2, 3)

A: As per the company guidelines we can solve one question. I hope that the given solution will help…

Q: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

A: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

Q: Question 2 Solve for x: a) 5 – 10x = 3x2 %3D

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Q: Which of the following representations of a quadratic has complex roots? Oal 9x2 + 33 = 0 b) -2.5 -2…

A: Hello! Thank you for the question but as per our honor code, we'll able to solve only three subparts…

Q: Find the largest area (sq. units) of the rectangle whose base is on the x-axis and its other two…

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Q: Find all real and complex solutions to the equation   x^3 − 3x^2 − 10x + 24 =0

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Q: QUESTION 3 Use the Quadratic formula to find TWO solutions to 2x2+4x – 11=0. Select them from the…

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Q: Answer the following: 1. Characterize the roots of the following quadratic equations using the…

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Q: Which of the following representation of a quadratic has a complex roots?

A: The given quadratic equation is: 9x2+33=0 To find its root simplify the given equation 9x2+33=0.…

Q: Write the equation of the parabola that has the same shape as f(x) = - 4x but with vertex (7,3) in…

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Q: Show that the equation  x4 + 4x + c =0 has at most tworeal roots.

A: Given: The method of contradiction is used to prove that the above equation has at most  two roots.

Q: List the roots of the parabola: y = x² + 2x + 5 In other words, list the solutions of the equation:…

A: The roots of a quadratics equation ax2+bx+c=0 is given by, x=-b±b2-4ac2a

Q: 8. Find the function that will generate the points on a parabola that opens down, has a base of 4…

A: A parabola has base 4 and height 6

Q: 6. Show that the quadratic equation ax² + b – a = 0 (a± 0) has two distinct real roots.

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Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function. 2(x -…

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Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x) =…

A: We have to find the coordinates of the vertex for the parabola defined by the quadratic function…

Q: find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x) =…

A: The equation for a parabola is written in vertex form as, In vertex form the vertex is given as…

Q: 5. Given the following parabola, f, -5 -4 -3 -2 -1 -6-5 -4 3-2 -1, 0 1 234 5/ 67 -2 -3 -6

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Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)…

A: The quadratic function is given by fx = 2x-32+1 To evaluate : The vertex of the parabola defined by…

Q: Find an equation for the parabola shown in the figure.

A: Given: The focus F-2,1 and directrix x=3 of the parabola, To find: The equation of the parabola.

Q: Which of the following representations of a quadratic has complex roots? Oal 9z2 + 33 = 0 y -2.5 -2…

A: For finding which quadratic equation have complex, we find roots of all equation given in options…

Q: If a is greater than or equal to zero the equation of the parabola is of the form?

A: Parabola is a three dimensional curve, where any point is at fix distance from the point called…

Q: Solve for complex x. e^(x^2+4x)=8

A: Solve the equation e^(x^2+4x) = 8 for complex x as follows.

Q: The parabola y = kx2 – 3x + (k+2) has two distinct real roots. What set of values can k be?

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Q: OShow that every cubic equation of the form x³ + bx2 + c = 0 where b and c are real numbers has at…

A: Given: x3+bx2+c=0, where b and c are real numbers. The objective is to show that every cubic…

Q: The a value in the function f(x) = 2x2 makes the parabola %3D O more wider moves it left

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Q: Express the equation of the parabola below in standard form. x2+6x−2y+1=0

A: Recall: Equation of parabola:         y-k2=4ax-h where (h,k) is the vertex and parabola is open in…

Q: Complete the table below. Show your solutions. Equation 1. x2 + 5x +4 = 0 2. 2x2 + x-21 = 0 3.4x2 +…

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Q: у" — Зху' + 2у %3D 0

A: Given the eqn. y"-3xy'+2y=0        .....(A) then,  y=c0+c1x+c2x2+3c3x3+......=Σn=1ςnCn xn-1…

Q: Find the standard form of the equation of the parabola that has a vertex at (1,-3) and passes…

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Q: 4 3 1 -3 -2 -1 0 1 2 3 4 -1

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Q: What is/are the value/s of k if the sum of the roots of x2 + kx + 3x = 1 is 3?

A: We know that if α and β be roots of a quadratic equationax2+bx+c=0, then α+β=-ba and αβ=caHere, the…