The quadratic function in vertex form is [tex]y=\frac{1}{2} (x-5)^{2}-2[/tex].
Solution:
The equation of a quadratic in vertex form is [tex]y=a(x-h)^{2}+k[/tex].
where (h, k) are the coordinates of the vertex and "a" is a multiplier.
Here (h, k) = (5, –2)
Substitute this in the vertex form.
[tex]y=a(x-5)^{2}+(-2)[/tex]
[tex]y=a(x-5)^{2}-2[/tex] – – – – (1)
Passes through the point (7, 0).
Here x = 7 and y = 0.
Substitute this in equation (1), we get
[tex]0=a(7-5)^{2}-2[/tex]
[tex]0=4a-2[/tex]
Add 2 on both sides.
2 = 4a
Divide 2 on both sides, we get
[tex]$a=\frac{1}{2}[/tex]
Substitute the value of a in equation (1),
[tex]$y=\frac{1}{2} (x-5)^{2}-2[/tex]
The quadratic function in vertex form is [tex]y=\frac{1}{2} (x-5)^{2}-2[/tex].
