Answer:
[tex]a=-\frac{1}{8}[/tex]
Step-by-step explanation:
Given
See attachment for graph
Required
Write the vertex form and then solve for
The general equation is:
[tex]y = a(x - h)^2 + k[/tex]
From the attachment, the vertex is at:
[tex](h,k) = (24,50)[/tex]
i.e.
[tex]h = 24; k= 50[/tex]
Considering point:
[tex](x,y) = (4,0)[/tex]
i.e.
[tex]x=4;y=0[/tex]
Substitute these values in [tex]y = a(x - h)^2 + k[/tex]
[tex]0 = a(4 - 24)^2 + 50[/tex]
[tex]0 = a(- 20)^2 + 50[/tex]
[tex]0 =a(400) + 50[/tex]
[tex]0 = 400a + 50[/tex]
Solve for a
[tex]400a = -50[/tex]
Make a the subject
[tex]a=-\frac{50}{400}[/tex]
[tex]a=-\frac{1}{8}[/tex]
