Finding Zeros of Quadratics

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 does it mean to find the zeros of a quadratic function?

Back

Finding the zeros of a quadratic function means determining the values of x for which the function equals zero (f(x) = 0).

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What is factoring in the context of quadratics?

Back

Factoring is the process of rewriting a quadratic expression as a product of its linear factors.

Front

How do you factor the quadratic x² + 4x - 21?

Back

The factors are (x + 7)(x - 3).

Front

What are the roots of the quadratic x² + 5x - 14?

Back

The roots are -7 and 2.

Front

How do you find the roots of a quadratic equation?

Back

You can find the roots by factoring, using the quadratic formula, or completing the square.

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 are the zeros of the function represented by the equation x² + 4x - 21?

Back

The zeros are -7 and 3.

Front

What does the discriminant of a quadratic equation tell us?

Back

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