Solving Quadratics (All methods)

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 ax² + bx + c = 0.

Front

What does it mean to complete the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q, making it easier to find the roots.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression of the form ax² + bx + c, find two numbers that multiply to ac and add to b, then rewrite the expression as (px + q)(rx + s).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac. It determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

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.

Front

What is the vertex form of a quadratic equation?

Back

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

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 axis of symmetry in a quadratic function?

Back

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

Front

How do you find the roots of a quadratic equation using the quadratic formula?

Back

Substitute the values of a, b, and c into the quadratic formula x = (-b ± √(b² - 4ac)) / (2a) and simplify to find the roots.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.