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

The quadratic function in vertex form is .

Solution:

The equation of a quadratic in  vertex form  is .

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.

– – – – (1)

Passes through the point (7, 0).

Here x = 7 and y = 0.

Substitute this in equation (1), we get

Add 2 on both sides.

2 = 4a

Divide 2 on both sides, we get

Substitute the value of a in equation (1),

The quadratic function in vertex form is .