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 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.

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.

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.

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.

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.

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.