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: $c=-\frac{3}{4}$

Step-by-step explanation:

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

$x=\frac{-b}{2a}$

In this case:

$a=4\\b=-10$

Substituting values, we get:

$x=\frac{-(-10)}{2(4)}=\frac{5}{4}$

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

Then:

$-7 = 4(\frac{5}{4})^2 -10(\frac{5}{4}) + c\\\\-7+\frac{25}{4}=c\\\\c=-\frac{3}{4}$