Algebra Test Quadratic Equations

Question 1

What are the solutions to x² - 5x + 6 = 0?

Accepted Answer

x = 2 and x = 3

Answer

Factor as (x - 2)(x - 3) = 0, giving x = 2 and x = 3.

Question 2

What is the vertex form of a quadratic equation?

Accepted Answer

y = a(x - h)² + k

Answer

Vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Question 3

What is the discriminant of 2x² - 4x + 2 = 0?

Accepted Answer

0

Answer

Discriminant = b² - 4ac = (-4)² - 4(2)(2) = 16 - 16 = 0.

Question 4

A discriminant of zero means a quadratic has:

Accepted Answer

One repeated real root

Answer

A discriminant of zero means exactly one repeated real root where the parabola just touches the x-axis.

Question 5

Solve x² - 9 = 0 by factoring.

Accepted Answer

x = ±3

Answer

Factor as (x - 3)(x + 3) = 0, giving x = 3 or x = -3.

Algebra Test Practice Test