Unit 9 Solving Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

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.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

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 the direction it opens.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

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 equation x = -b/(2a).

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph crosses the x-axis, found by solving the equation ax² + bx + c = 0.

Front

What is the quadratic formula?

Back

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

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which determines the nature of the roots.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.