Standard and Vertex Forms and Graphs of Quadratic Functions

Front

In the vertex form of a quadratic function, ___ is the vertex and ___ is the axis of symmetry.

Back

(h,k); x=h

Front

Why use vertex form?

Back

Vertex form shows the vertex of a quadratic equation in respect to its parent function, f(x) = x².

Front

Identify the vertex and axis of symmetry for the function f(x) = -(x + 5)² - 1.

Back

Vertex: (-5, -1); Axis of symmetry: x = -5

Front

For the quadratic inequality y ≥ 4(x+1)² - 7, give the vertex and axis of symmetry.

Back

Vertex: (-1, -7); Axis of symmetry: x = -1

Front

If a parabola has a vertex at (-3, 2), where is the axis of symmetry?

Back

x = -3

Front

What is the standard form of a quadratic function?

Back

f(x) = ax² + bx + c, where a, b, and c are constants.

Front

How do you convert from vertex form to standard form?

Back

Expand f(x) = a(x-h)² + k to get f(x) = ax² - 2ahx + (ah² + k).

Front

What does the 'a' value in the vertex form indicate about the parabola?

Back

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

Front

What is the axis of symmetry for the quadratic function f(x) = 2x² + 4x + 1?

Back

x = -b/(2a) = -4/(2*2) = -1.

Front

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

Back

Use the formula (h, k) where h = -b/(2a) and k = f(h).