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.

Front

How do you find the roots of a quadratic equation?

Back

To find the roots of a quadratic equation, you can use factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

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

Front

What does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression means rewriting it as a product of its linear factors.

Front

What is the GCF (Greatest Common Factor)?

Back

The GCF is the largest factor that divides two or more numbers or expressions.

Front

How do you determine the GCF of 4x² - 24?

Back

The GCF of 4x² - 24 is 4, since 4 is the largest number that divides both terms.

Front

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

Back

The first step is to find the GCF, which is 3, allowing you to factor it as 3[x² + 2x - 3].

Front

What are the steps to graph a quadratic function?

Back

1. Identify the vertex. 2. Find the x-intercepts (zeros). 3. Determine the y-intercept. 4. Plot points and draw the parabola.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How do you find the x-intercepts of a quadratic function?

Back

Set the quadratic equation equal to zero and solve for x.