Question

move at least one of the 3 guide points below to complete the graph of $y = \frac{3}{2}\sqrt{x} + 7$. moving the red points changes the vertical stretch or compression. moving the blue point shifts the function left/right/up/down. click the buttons below to start over or reflect over the x-axis.
reset reflect over x-axis

Explanation:

Step1: Find base point (x=0)

Substitute $x=0$ into $y=\frac{3}{2}\sqrt{x}+7$:
$y=\frac{3}{2}\sqrt{0}+7=7$
Base point: $(0,7)$

Step2: Find 1st stretched point (x=1)

Substitute $x=1$ into $y=\frac{3}{2}\sqrt{x}+7$:
$y=\frac{3}{2}\sqrt{1}+7=\frac{3}{2}+7=8.5$
Point: $(1,8.5)$

Step3: Find 2nd stretched point (x=4)

Substitute $x=4$ into $y=\frac{3}{2}\sqrt{x}+7$:
$y=\frac{3}{2}\sqrt{4}+7=\frac{3}{2}\times2+7=3+7=10$
Point: $(4,10)$

Step4: Adjust guide points

1. Move the blue shift point from $(0,0)$ to $(0,7)$.
2. Move the first red stretch point from $(1,1)$ to $(1,8.5)$.
3. Move the second red stretch point from $(4,2)$ to $(4,10)$.

Answer:

1. Blue shift point: $(0,7)$
2. First red stretch point: $(1,8.5)$
3. Second red stretch point: $(4,10)$

When these points are placed, the graph of $y=\frac{3}{2}\sqrt{x}+7$ will be correctly plotted.