Algebra 2 Final Exam

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It determines the nature of the roots of the equation.

Front

How do you factor a quadratic expression of the form ax² + bx + c?

Back

To factor, find two numbers that multiply to ac and add to b. Rewrite the middle term using these numbers and factor by grouping.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real root (a repeated root).

Front

What does it mean if the discriminant is negative?

Back

If the discriminant is negative, the quadratic equation has no real roots (the roots are complex).

Front

How do you solve a system of equations graphically?

Back

To solve graphically, plot both equations on the same graph and identify the point(s) where they intersect.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, found at the point (h, k) in the vertex form y = a(x - h)² + k.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the factored form of a quadratic equation?

Back

The factored form is expressed as a(x - r₁)(x - r₂), where r₁ and r₂ are the roots of the equation.