Evaluating Quadratic Functions

Front

What is a quadratic function?

Back

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

Front

How do you evaluate a quadratic function at a specific point?

Back

To evaluate a quadratic function at a specific point, substitute the value of x into the function and simplify.

Front

Evaluate g(x) = x² - 4 for g(5).

Back

g(5) = 5² - 4 = 25 - 4 = 21.

Front

Evaluate f(t) = -2t² + 1 for f(-3).

Back

f(-3) = -2(-3)² + 1 = -2(9) + 1 = -18 + 1 = -17.

Front

Evaluate f(x) = x² - 5x for f(4).

Back

f(4) = 4² - 5(4) = 16 - 20 = -4.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola (upward or downward). It can be found using the formula x = -b/(2a).

Front

Solve for x: (x + 6)² = 49.

Back

x + 6 = ±7; x = 1 or x = -13.

Front

Evaluate f(x) = x² for f(-8).

Back

f(-8) = (-8)² = 64.

Front

What does the 'a' value in a quadratic function indicate?

Back

The 'a' value determines the direction of the parabola: if a > 0, the parabola opens upward; if a < 0, it opens downward.

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).