Question

The c value of the function that represents the graph above is…Write the equation that would represent the graph shown above.

Answer 1

we have that

Part A ----> quadratic

Part B ----> positive, because open upward

Part C ---> c value is negative , because represents the y-intercept (y-intercept is (0,-3)

Part D

write the equation

The equation in vertex form is equal to

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

where

(h,k) is the vertex

a is the leading coefficient

Looking at the graph

The vertex is the point (1,-4)

substitute

`y=a(x-1)^2-4`

Find out the value of a

we need one point

looking at the graph

we take the point (3,0)

substitute

`\begin{gathered} 0=a(3-1)^2-4 \\ 0=a(4)-4 \\ 4a=4 \\ a=1 \end{gathered}`

therefore

`\begin{gathered} y=(x-1)^2-4 \\ y=x^2-2x+1-4 \\ y=x^2-2x-3 \end{gathered}`