Key Features, Standard Form, and Vertex Form Quadratic Functions

Front

What is the graph of a quadratic function called?

Back

Parabola

Front

Order the following quadratic functions from narrowest to widest: y = 4x^2, y = 2x^2 - 2, y = x^2, y = 0.5x^2.

Back

y = 4x^2, y = 2x^2 - 2, y = x^2, y = 0.5x^2.

Front

How does the function y = 5x^2 compare to the parent function y = x^2?

Back

Narrower

Front

Which quadratic function has a vertex below the origin and opens upward? y = -x^2 + 3, y = -x^2 - 1, y = x^2 + 5, y = x^2 - 2.

Back

y = x^2 - 2.

Front

What is the range of the quadratic function y = x^2 - 2?

Back

y ≥ -2.

Front

What is the standard form of a quadratic function?

Back

The standard form is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the vertex form of a quadratic function look like?

Back

The vertex form is y = a(x - h)^2 + k, where (h, k) is the vertex.

Front

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

Back

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

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line that divides the parabola into two mirror images, given by x = -b/(2a).

Front

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

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h).