Solving Quadratic Equations by Factoring and Graphing

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 are the zeros of a function?

Back

The zeros of a function are the values of x for which the function f(x) = 0. They are the x-intercepts of the graph.

Front

How do you find the zeros of a quadratic equation by factoring?

Back

To find the zeros by factoring, express the quadratic in the form (x - p)(x - q) = 0, where p and q are the zeros. Then, set each factor to zero and solve for x.

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

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards.

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).

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

How can you determine the number of real solutions of a quadratic equation?

Back

The number of real solutions can be determined using the discriminant (b² - 4ac): if it's positive, there are two solutions; if zero, one solution; if negative, no real solutions.

Front

What is factoring in the context of quadratic equations?

Back

Factoring involves rewriting the quadratic equation as a product of two binomials, allowing for easier identification of the zeros.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the function at x = 0.