Question

Write a quadratic function in vertex form whose graph has the vertex (5,−2) and passes through the point (7,0).

Answer 1

The quadratic function in vertex form is $y=\frac{1}{2} (x-5)^{2}-2$.

Solution:

The equation of a quadratic in  vertex form  is $y=a(x-h)^{2}+k$.

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.

$y=a(x-5)^{2}+(-2)$

$y=a(x-5)^{2}-2$ – – – – (1)

Passes through the point (7, 0).

Here x = 7 and y = 0.

Substitute this in equation (1), we get

$0=a(7-5)^{2}-2$

$0=4a-2$

Add 2 on both sides.

2 = 4a

Divide 2 on both sides, we get

$a=\frac{1}{2}$

Substitute the value of a in equation (1),

$y=\frac{1}{2} (x-5)^{2}-2$

The quadratic function in vertex form is $y=\frac{1}{2} (x-5)^{2}-2$.