Graphing f(x) = ax^2 & f(x) = ax^2

Graphing f(x) = ax² & f(x) = ax² +c

By Aileen Freeman

​(x) = ax^2

Multiple Choice

$$y\ =\ ax^2\ +\ c\ \$$  

• linear 

• absolute value 

• quadratic 

• exponential 

Multiple Choice

The U-shaped graph of a quadratic function is called

• parabola

• hyperbola

• utopia

• linear

Multiple Choice

The lowest or highest point on a parabola is the

• origin

• x-axis

• y-axis

• vertex

Multiple Choice

The vertical line that divides the parabola into two symmetric parts is called the

• vertex

• increasing axis

• decreasing axis

• axis of symmetry

Multiple Choice

What is the domain of the given function?

• All real numbers

• -4 < x < 4

• x > 0

• x < 0

Multiple Choice

Identify the vertex

• (0 , 0)

• (-2 , 0)

• (2 , 0)

• (0 , -4)

Multiple Choice

Which choice describes the transformation of the parent function  $$f\left(x\right)=x^2$$  to  $$g\left(x\right)=0.45x^2$$  

• Vertical stretch by 0.45 (more narrow)

• Vertical shrink by 0.45 (wider)

• Reflection over x-axis

• None of these

Multiple Choice

Which choice describes the transformation of the parent function $$f\left(x\right)=x^2$$  to  $$g\left(x\right)=-3x^2$$   ?

• Reflection over x-axis and Vertical shrink by 3

• Reflection over x-axis

• Reflection over x-axis and Vertical stretch by 3

• Vertical stretch by 3

Multiple Choice

Compared to the Quadratic parent function, f(x) = x², how was function g transformed?

g(x) = x² + 2

• horizontal shift up

• vertical shift up

• horizontal shift down

• vertical shift down

Multiple Choice

In the vertex form f(x) = ax ² + c , what does the "c" value do?

• Shifts the function left or right

• Reflects over the x-axis

• Vertical stretch or compression

• Shifts the function up or down

Multiple Choice

Choose the correct graph of  $$f\left(x\right)\ =\ x^2+3$$  .

Use the Desmos Graphing Calculator!

Multiple Choice

Choose the correct graph of $$f\left(x\right)\ =\ -3x^2+2$$

Use the Desmos Graphing Calculator!