Question

question
move at least one of the 5 guide points below to complete the graph of $y = 5x^2 + 5$. 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: Identify vertex of base function

The base function is $y=x^2$, vertex at $(0,0)$. For $y=5x^2+5$, vertical shift up 5: vertex becomes $(0, 0+5)=(0,5)$.

Step2: Find points via vertical stretch

Take $x=1$: $y=5(1)^2+5=10$, so point $(1,10)$.
Take $x=-1$: $y=5(-1)^2+5=10$, so point $(-1,10)$.
Take $x=2$: $y=5(2)^2+5=25$, so point $(2,25)$.
Take $x=-2$: $y=5(-2)^2+5=25$, so point $(-2,25)$.

Step3: Relate to graph points

• Move the blue vertex point from $(0,0)$ to $(0,5)$.
• Move the red points at $(1,1)$ to $(1,10)$, $(-1,1)$ to $(-1,10)$, $(2,4)$ to $(2,25)$, $(-2,4)$ to $(-2,25)$.

Answer:

1. Shift the blue vertex point to $(0, 5)$
2. Move the red point at $(1,1)$ to $(1,10)$
3. Move the red point at $(-1,1)$ to $(-1,10)$
4. Move the red point at $(2,4)$ to $(2,25)$
5. Move the red point at $(-2,4)$ to $(-2,25)$