Quadratic Functions

Front

Define Roots, Zeros, and Solutions

Back

Where the parabola intersects the x-axis.

Front

Define Vertex

Back

The highest or lowest point on the graph.

Front

What is the significance of the ordered pair (2, -4) to the graph?

Back

It is the vertex.

Front

What is the maximum height of the pathway represented by the equation h = -16t^2 + 80t + 25?

Back

h = 125 feet.

Front

Describe the transformation of the function: -3(x+4)^2-1

Back

Reflect over the x-axis, stretch by 3, left: 4, down: 1.

Front

What is the standard form of a quadratic function?

Back

f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

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

Back

The direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

How do you find the axis of symmetry for a quadratic function?

Back

x = -b/(2a), where f(x) = ax^2 + bx + c.

Front

What is the quadratic formula used for?

Back

To find the roots of a quadratic equation: x = (-b ± √(b^2 - 4ac)) / (2a).

Front

What is the significance of the discriminant (b^2 - 4ac)?

Back

It determines the nature of the roots: two real roots if > 0, one real root if = 0, and no real roots if < 0.