Solving Quadratics

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x that make the function equal to zero. They are also known as the roots of the equation.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is the Zero-Product Property?

Back

The Zero-Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you find the zeros of the quadratic equation x² - 4 = 0?

Back

To find the zeros, set the equation to zero: x² - 4 = 0. Factor it as (x - 2)(x + 2) = 0. Thus, the zeros are x = 2 and x = -2.

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 the discriminant tell you about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

Solve the quadratic equation: x² + 5x + 6 = 0

Back

The solutions are x = -2 and x = -3.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you complete the square for the equation x² + 6x + 5 = 0?

Back

To complete the square, rewrite as (x + 3)² - 4 = 0, leading to x + 3 = ±2, thus x = -1 or x = -5.

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 x = -b/(2a).