Solving Quadratics (All Methods)

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

What are the zeros of a quadratic equation?

Back

The zeros (or solutions) of a quadratic equation are the values of x that make the equation equal to zero.

Tags

CCSS.HSA-REI.B.4B

Front

What is the quadratic formula?

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

What does the discriminant tell us?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

What is the zero product property?

Back

The zero product property states that if ab = 0, then either a = 0 or b = 0.

Tags

CCSS.HSA-REI.B.4B

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form (x - p)(x - q) = 0, then set each factor to zero: x - p = 0 or x - q = 0.

Tags

CCSS.HSA-REI.B.4B

Front

What is completing the square?

Back

Completing the square is a method to solve quadratic equations by rewriting the equation in the form (x + p)² = q.

Tags

CCSS.HSA-REI.B.4B

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 axis of symmetry?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by x = -b/(2a).