Solve a Quadratic by Factoring, Quadratic Formula, and Graph

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x that make the function equal to zero. They are also known as the roots or x-intercepts.

Front

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

Back

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

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 tell you about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if it's positive, there are two distinct real roots; if it's zero, there is one real root; if it's negative, there are no real roots.

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

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

Back

You can determine the number of solutions by calculating the discriminant: if it's positive, there are two solutions; if it's zero, there is one solution; if it's negative, there are no real solutions.

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 are x-intercepts?

Back

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

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.