Alg Unit 4B Day 3 Graphing Quadratics

Open Ended

Move one red ball to turn the sequence 1-2-3-4 into 4-3-2-1.

Let's review previous classes

Multiple Choice

Find the equation of the parabola that has moved...

5 units to the right from the parent function y = x²

• $$y=x^2+5$$

• $$y=x^2-5$$

• $$y=\left(x+5\right)^2$$

• $$y=\left(x-5\right)^2$$

Multiple Choice

Find the equation of the parabola that has moved 3 units to the left moved 5 units up from the parent function y = x²

• $$y=\left(x+3\right)^2+5$$
  

• $$y=\left(x+5\right)^2+3$$

• $$y=\left(x-3\right)^2+5$$

• $$y=\left(x+5\right)^2-3$$

Multiple Choice

Find the equation of the parabola that has compressed by factor of 2 moved 3 units to the left moved 4 units up from the parent function y = x²

• $$y=\frac{1}{2}\left(x+3\right)^2+4$$
  

• $$y=\frac{1}{2}\left(x-3\right)^2+4$$

• $$y=2\left(x+3\right)^2+4$$

• $$y=2\left(x-3\right)^2+4$$

Multiple Choice

Given f(x) = x² - 1,

what is the value of f(10)?

• 100

• 101

• 99

• 9

Multiple Choice

Given f(x) = (2 + x )²,

what is the value of f(-3)?

• 1

• 25

• -1

• 5

​l

Multiple Choice

What is the domain of the function?
*Hint: Domain is the set of all x-values included in the function.

• x ≥ 3

• x ≤ 3

• All real numbers
• -1 ≤ x ≤5

Multiple Choice

What is the range of the function?

*Hint: Range is all of the y-values included in the function.

• $$y\le3$$
  

• $$y\ge3$$

• All real numbers

• -6 ≤ y ≤ 3

Multiple Choice

Identify the domain and range of the function.

• Domain: -6 ≤ x ≤ 2

  Range: -3 ≤ y ≤ 5

• Domain: All real number

  Range: -3 ≤ y ≤ 5

• Domain: All real numbers

  Range: y ≤ 3

• Domain: All real numbers

  Range: $$y\ge-3$$

Multiple Select

y = 3x² - 5x + 2

What are the end behaviors for this function?

• As x gets bigger, y gets bigger.

• As x gets bigger, y gets smaller.

• As x gets smaller, y gets bigger.

• As x gets smaller, y gets smaller.

Multiple Choice

Describe the end behavior of the graph.

• $$x→∞,\ y→∞\$$

  $$x→∞,\ y→\ ⁻∞$$

• $$x→∞,\ \ y→∞$$

  $$x→\ ⁻∞,\ \ y→∞$$

• None of these

• $$x→∞,\ \ y→\ ⁻∞$$ $$x→∞,\ \ y→\ ⁻∞$$

Multiple Choice

Describe the end behavior of the graph.

• $$x→∞,\ \ \ y→\ ⁻∞$$

  and

  $$x→\ ⁻∞,\ y→\ ⁻∞$$

• x →∞, y→∞

  and

  x→⁻∞, y→∞

• x →∞, y→∞

  and

  x→ ⁻∞, y→0

• $$x→∞,\ y→∞$$

  and

  $$x→⁻∞,\ y→⁻∞$$

​Intervals of increasing or decreasing

Multiple Select

f(x) = -x² - 4x - 7

What are the intervals of increasing and decreasing for this function?

• Increasing from

  $$x=-2\ \rightarrow+∞$$

• Decreasing from

  $$x=-2\ \rightarrow\ ∞$$

• Increasing from

  $$-∞\ to\ x=-2$$

• Decreasing from

  $$-∞\ to\ x=-2$$