Solve Quadratics by Factoring

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic equation?

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

What are the solutions of the equation (x - 5)(x + 6) = 0?

Back

The solutions are x = 5 and x = -6.

Tags

CCSS.HSA-REI.B.4B

Front

How do you find the zeros of a quadratic function?

Back

To find the zeros of a quadratic function, set the equation equal to zero and solve for x, either by factoring, using the quadratic formula, or completing the square.

Tags

CCSS.HSF-IF.C.7C

Front

What is the quadratic formula?

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if it's positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Tags

CCSS.HSA-REI.B.4B

Front

What are the steps to solve a quadratic equation by factoring?

Back

1. Write the equation in standard form (ax² + bx + c = 0). 2. Factor the quadratic expression. 3. Set each factor equal to zero. 4. Solve for x.

Tags

CCSS.HSA-REI.B.4B

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 it is negative.

Tags

CCSS.HSF-IF.C.7A

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).