Review Unit 8

Review Unit 8

Time to Review!!!

Multiple Choice

When is your Unit 8 Test?

• Tomorrow

• Wednesday

• Friday

• Monday

Multiple Choice

Which function is represented by the graph?

• $$y=3x^2$$

• $$y=\frac{1}{3}x^2$$

• $$y=-3x^2$$

• $$y=-\frac{1}{3}x^2$$

Why?

Multiple Choice

Which equation represents the axis of symmetry for the graph?

• x = 1

• x = 2.5

• y = -1.25

• y = -0.5

Why?

The axis of symmetry splits the graph in half. It is half way between the two x-intercepts.

Multiple Choice

The graph of  $$y=x^2$$  was transformed to create the graph of  $$y=\left(x-3\right)^2$$  . Which of these describes the transformation?

• A vertical shift up 3 units

• A vertical shift down three units

• A horizontal shift to the left 3 units

• A horizontal shift to the right 3 units

Why?

Multiple Choice

Which statement(s) describe the function  $$f\left(x\right)=x^2+6x-4$$  ?

I. The graph opens up II. The axis of symmetry is x = -3. III. The maximum is at (-3, -13) 

• II and III only

• I and III only

• I and II only

• II only

Why?

I. The graph opens up (true)

II. The axis of symmetry is x=-3 (true)

III. The maximum is (-3, -13).

FALSE! It's the minimum!

Multiple Choice

The graph of  $$f\left(x\right)=x^2$$  is transformed to create  $$h\left(x\right)=4f\left(x\right)$$  . Which graph represents f and h?

Why?

Multiple Choice

Which quadratic function represents a parabola that has a vertex of (4, 10) and goes through (2, 0)?

• $$y=\frac{5}{2}\left(x-4\right)^2-10$$

• $$y=\frac{5}{2}\left(x-4\right)^2+10$$

• $$y=\frac{5}{2}\left(x+4\right)^2+10$$

• $$y=\frac{5}{2}\left(x+4\right)^2-10$$

Why?

When you graph the correct answer, it goes through the points described.

Multiple Choice

The graph of $$f\left(x\right)=x^2$$  was transformed to make the graph of  $$h\left(x\right)=-\left(\frac{x}{2}\right)^2$$  . Which of these describes the transformation?

• Reflection over the x-axis and a horizontal stretch

• Reflection over the y-axis and a horizontal stretch

• Reflection over the x-axis and a horizontal shrink

• Reflection over the y-axis and a horizontal shrink

Why?

The transformed graph (blue) is reflected over the x-axis. Graphs will NEVER be reflected over y. The graph is also wider, which is called horizontal stretch.

Multiple Choice

What is the range of the graph below?

• All real numbers

• All real numbers less than 2 and greater than -2

• y > -9

• y < -9

Why?

The range refers to y. The minimum of the graph is (0, -9), so all y-values are -9 and greater.

Multiple Choice

The graph shows the height in feet of an object above the ground t seconds after it was launched. What is the equation?

• $$h\left(t\right)=-16t^2-81t-64$$

• $$h\left(t\right)=-16t^2+81t-64$$

• $$h\left(t\right)=-16t^2-81t$$

• $$h\left(t\right)=-16t^2+81t$$

Why?

When you graph each of the possible equations, the correct answer matches the graph that was shown.

Multiple Choice

How does the graph of $$q\left(x\right)=-\frac{1}{4}x^2$$  compare to the parent function?

• q(x) opens up and is narrower

• q(x) opens up and is wider

• q(x) opens down and is narrower

• q(x) opens down and is wider

Why?

The graph of q(x) (purple) is clearly wider and opens the opposite direction compared to the parent function.

Multiple Choice

The profit of a donut shop can be represented by  $$y=-0.08\left(x-50\right)^2+200$$  where x is the donuts sold and y is the profit. What is the maximum profit of this donut shop?

• $50

• $100

• $200

• $80

Why?

When you graph it, the maximum is at (50, 200). This represents 50 donuts, which costs $200. $200 is therefore the maximum profit.

Multiple Choice

Jordan wants to determine a quadratic function with a vertex of (5, 4) that passes through (0, 16.5). He writes his answer in vertex form. What will be the values of a, h, and k?

• a = 1/2; h=-5, k=4

• a = 1/2; h=5, k=4

• a = 1; h=-5, k=4

• a = 1; h=5, k=4

Fill in the Blanks

Why?

The graph passes through (0, -2) on the y-axis. The y-value of this intercept is -2.