Question

Which of the following could be the equation of the graph below? See graph below select the answer

Answer 1

`y = 2( {x - 4)}^(2) - 3`

Step-by-step explanation

The function equation of a parabola that opens up in vertex form is given by

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

where (h,k) is the vertex and 'a' is the leading coefficient.

The given graph is a parabola that opens up and has its vertex at (4,-3).

This implies that, h=4 and y=-3

We substitute these values into the vertex form to obtain,

`y =a( {x - 4)}^(2) + - 3`

This simplifies to,

`y =a( {x - 4)}^(2) - 3`

The graph also contains (3,-1). We plug x=3 and y=-1 into the equation to find the value of 'a'.

`- 1=a( {3 - 4)}^(2) - 3`

`- 1 + 3 = a( { - 1})^(2)`

`2 = a`

We substitute this value to get:

`y = 2( {x - 4)}^(2) - 3`

The last choice is correct.