Answer: [tex]c=-\frac{3}{4}[/tex]
Step-by-step explanation:
Find the x-coordinate of the vertex with this formula:
[tex]x=\frac{-b}{2a}[/tex]
In this case:
[tex]a=4\\b=-10[/tex]
Substituting values, we get:
[tex]x=\frac{-(-10)}{2(4)}=\frac{5}{4}[/tex]
Now we can substitute the coordinates of the vertex into the equation [tex]y = 4x^2 -10x + c[/tex] and then solve for "c".
Then:
[tex]-7 = 4(\frac{5}{4})^2 -10(\frac{5}{4}) + c\\\\-7+\frac{25}{4}=c\\\\c=-\frac{3}{4}[/tex]
