Question

Given that, for all values of x,

2x^2 – 3x + 21 = a(x - b)^2 + c
find the value of a, the value of b and the value of c.​

Answer 1

Explanation:

To find a, the leading coeffiecent of the quadratic is a.

So a is 2.

To find b, we must use the formula

`- (b)/(2a)`

`( - ( - 3))/(2(2)) = (3)/(4)`

So b=3/4.

To find c, plug in 3/4 into the function,

which we get

`2( (9)/(16) ) - 3( (3)/(4) ) + 21`

`(9)/(8) - (9)/(4) + 21 = (9)/(8) - (18)/(8) + 21 = - (9)/(8) + 21 = 19.875`

So c=19.875