Question

A quadratic function has its vertex at the point ( − 2 , 6 ) . The function passes through the point ( 0 , 3 ) . Find the quadratic and linear coefficients and the constant term of the function.

The quadratic coefficient is ___
The linear coefficient is ___
The constant term is ___

Answer 1

quadratic coefficient =
`-(3)/(4)`

linear ... = -3

constant term = 3

Explanation:

1. given the vertex, set up the function in vertex form (a is unknown):

y = a(x + 2)² + 6

2. Substitute (0,3) for x and y in the equation and solve to find a:

3 = a(0+2)²+6

3 = 4a+6

-3 = 4a

a = -3/4

3. Substitute -3/4 for a in step 1:
`y=-(3)/(4)(x+2)^(2)+6`

4. Convert equation to standard form using the Order of Operations:

`y=-(3)/(4)x^(2)-3x+3`