Solving 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 can be found by factoring, using the quadratic formula, or graphing.

Front

Solve for x: 3x² - 192 = 0

Back

x = -8 or x = 8

Front

Find the zeros of the equation: (x+10)(x-2) = 0

Back

x = -10 and x = 2

Front

Solve using Zero-Product Property: (x-11)(5x+1) = 0

Back

x = 11 or x = -1/5

Front

Solve: 2x² + 17x + 21 = 0

Back

x = -7, x = -3/2

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of the quadratic equation ax² + bx + c = 0.

Front

What does it mean for a quadratic to be factored?

Back

Factoring a quadratic means expressing it as a product of two binomials, such as (x - p)(x - q) = 0, where p and q are the zeros.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you determine if a quadratic opens upwards or downwards?

Back

A quadratic opens upwards if the coefficient of x² (a) is positive and downwards if a is negative.

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).