Solving Quadratics by Graphing and Factoring

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x for which the function equals zero. They are 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 factoring in the context of solving quadratics?

Back

Factoring is the process of rewriting a quadratic equation in the form (x - p)(x - q) = 0, where p and q are the zeros of the function.

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 the vertex of a parabola represent?

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 can you determine the direction of a parabola?

Back

The direction of a parabola is determined by the sign of the coefficient 'a' in the quadratic equation. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

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 is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula. It determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form (x - p)(x - q) = 0, then set each factor equal to zero and solve for x.

Front

What are the steps to graph a quadratic function?

Back

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