Finding Zeros of Quadratics

Front

What are the zeros of a quadratic equation?

Back

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

Front

How do you factor the quadratic expression x² + x - 2?

Back

(x - 1)(x + 2)

Front

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

Back

(x + 7)(x - 3)

Front

What are the x-intercepts of a quadratic equation known as?

Back

Zeros

Front

How do you factor the quadratic expression x² - x - 20?

Back

(x - 5)(x + 4)

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.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function.

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

What is the quadratic formula used for?

Back

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

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 real roots; if zero, one real root; if negative, no real roots.