Question

What is the value of c in the equation y = 4x^2 -10x + c if the y-coordinate of the vertex is -7

Answer 1

Answer:
`c=-(3)/(4)`

Explanation:

Find the x-coordinate of the vertex with this formula:

`x=(-b)/(2a)`

In this case:

`a=4\\b=-10`

Substituting values, we get:

`x=(-(-10))/(2(4))=(5)/(4)`

Now we can substitute the coordinates of the vertex into the equation
`y = 4x^2 -10x + c` and then solve for "c".

Then:

`-7 = 4((5)/(4))^2 -10((5)/(4)) + c\\\\-7+(25)/(4)=c\\\\c=-(3)/(4)`