Solving Quadratics by Graphing and Factoring

Front

What is a zero of a quadratic function?

Back

A zero of a quadratic function is a value of x that makes the function equal to zero. It represents the x-intercepts of the graph.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find the zeros of a quadratic function by graphing?

Back

To find the zeros by graphing, plot the quadratic function on a coordinate plane and identify the points where the graph intersects the x-axis.

Tags

CCSS.HSF-IF.C.7A

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 does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression means rewriting it as a product of two binomials.

Front

What is the first step in factoring the quadratic expression 3x² + 6x - 9?

Back

The first step is to find the greatest common factor (GCF), which is 3, and factor it out: 3[x² + 2x - 3].

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the function crosses the x-axis, corresponding to the zeros of the function.

Tags

CCSS.HSF-IF.C.7A

Front

How can you verify the solutions of a quadratic equation?

Back

You can verify the solutions by substituting them back into the original equation to see if they satisfy it.

Tags

CCSS.HSA-REI.B.4B

Front

What is the relationship between the coefficients and the roots of a quadratic equation?

Back

The sum of the roots (solutions) is equal to -b/a and the product of the roots is equal to c/a, according to Vieta's formulas.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

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 does the discriminant of a quadratic equation tell you?

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.

Tags

CCSS.HSA-REI.B.4B