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

An equation of the function of this graph is equal to $y=1(x-5)^2 + 3$

Given the following data:

• Points on the x and y-axis = (8, 12).

• Vertex (h, k)= (5, 3).

How to write a function.

The vertex form of a quadratic equation can be used to write an equation of the function of a graph.

Mathematically, the vertex form of a quadratic equation is given by this formula:

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

Substituting the given parameters into the formula, we have;

$12=a(8-5)^2 + 3\\\\12=(3a)^2+3\\\\9a^2=12-3\\\\9a^2=9\\\\a^2=1$

a = 1.

For the equation:

$y=a(x-h)^2 + k\\\\y=1(x-5)^2 + 3$

Read more on vertex here: https://brainly.com/question/525947