Solving Quadratics and Complex Numbers

Christian is rewriting an expression of the form y = ax² + bx + c in the form y = a(x – h)² + k. Which of the following must be true?

• k and c have the same value

• the value of a remains the same

• h and k cannot both equal zero

• h is equal to one half –b

What is the first step when rewriting y = 6x² + 18x + 14 in the form y = a(x – h)² + k?

• x must be factored from 6x² + 18x

• 6 must be factored from 6x² + 14

• 16 must be factored from 18x + 14

• 6 must be factored from 6x² + 18x

Pablo graphs a system of equations. One equation is quadratic and the other equation is linear. What is the greatest number of possible solutions to this system?

• 0

• 1

• 4

• 2

Parabola A can be represented using the equation (x + 3)² = y, while line B can be represented using the equation y = mx + 9. Isabel claims one solution to the system of two equations must always be the vertex of parabola A.

Which best describes the reasonableness of her claim?

• Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the x-intercept of the equations, not the vertex.

• Isabel is correct because the y-intercept of line B is (0, 9) and the value of y when x = 0 in parabola A is 9.

• Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the y-intercept of the equations, not the vertex.

If the discriminant of a quadratic equation is equal to , which statement describes the roots?

• There is one real root.

• There are two complex roots.

• There is one complex root.

If , f(x)= square root x-3 which inequality can be used to find the domain of f(x)?

• 2x + 2x>0

• x-3>0

• x+3>0

Which equation can be simplified to find the inverse of y = 2x²?

• y=2x

• y=1/2

• x=2y^2

Which equation is the inverse of y = 100 – x²?

• y=+square root 100-x

• y=+10 square x

• y=+20square root x

if the domain of the square root function f(x) is x<7, which statement must be true

• the x term inside the radical have a negative coefficient

• 7 is subtracted from x term inside the radical term

• 7 is added to the radical term

what are the values of a,b,c in the quadratic equation -2x^2 + 4x-3=0

• a=4, b=-2, c=3

• a=-2, b=4, c=-3

• a=2, b=3, c=4