Question

Write the equation of the function whose graph is shown.

Answer 1

Answer:

$y=1(x-5)^2 + 3$

Step-by-step explanation:

Given : from the graph vertex is (5,3)

Also graph passes through point (8,12)

We use vertex form of quadratic equation

General vertex form is

$y=a(x-h)^2 + k$

vertex is (5,3)

h= 5 and k =3

So equation becomes $y=a(x-5)^2 + 3$

Now we need to find out 'a'

We use (8,12) to find out 'a'

Plug in x=8 and y = 12

$12=a(8-5)^2 + 3$

$12=a(3)^2 + 3$

12= 9a + 3

subtract 3 on both sides

9 = 9a

divide both sides by 9

so a=1

Final equation is

$y=1(x-5)^2 + 3$

Answer 2

Looks like (5, 3) is the vertex, and the graph passes through the point (8, 12)
y=a(x-5)^2+3
Next, use y=12 when x=8 to find out the value of a:
12=a(8-5)^2+3 => a=1
so y=(x-5)^2+3