Keystone Test Keystone Algebra: Polynomials and Quadratic Functions 2

Question 1

Which method can be used to find the roots of any quadratic equation?

Accepted Answer

Quadratic formula

Answer

The quadratic formula x = (−b ± √(b²−4ac)) / 2a works for any quadratic equation.

Question 2

What does the discriminant b² − 4ac tell you about a quadratic equation?

Accepted Answer

The number and type of solutions

Answer

The discriminant determines if there are two real, one real, or two complex solutions.

Question 3

What is the axis of symmetry of y = 2x² − 8x + 3?

Accepted Answer

x = 2

Answer

The axis of symmetry is x = −b/(2a) = −(−8)/(2·2) = 8/4 = 2.

Question 4

Which of the following correctly factors 2x² + 7x + 3?

Accepted Answer

(2x + 1)(x + 3)

Answer

Expanding (2x + 1)(x + 3) = 2x² + 6x + x + 3 = 2x² + 7x + 3.

Question 5

A parabola opens downward when the leading coefficient a is:

Accepted Answer

Negative

Answer

When a < 0 in y = ax² + bx + c, the parabola opens downward.

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