F.4 QUADRATIC FUNCTIONS

Since the function intercepts the x - axis at 3/2 and -1/2.
So the function is y = a(x - 3/2)(x + 1/2)
When x = 0, y = 9
so 9 = a(-3/2)(1/2)
so a = -36/3 = -12.
so y = - 12(x - 3/2)(x + 1/2) = - 12(x^2 - x - 3/4) = - 12x^2 + 12x + 9.
(b) By completing square method,
y = - 12(x^2 - x) + 9
= - 12[(x - 1/2)^2 - 1/4] + 9
= -12(x - 1/2)^2 + 3 + 9
so the vertex is (1/2, 12)

The x-intercepts of the graph of a quadratic function are 3/2 and -1/2 , and the y-intercept is 9

a.) find the quadratic function
Let Ax^2 + Bx + C = 0 be the function,
3/2 - 1/2 = -B/A => 1 = 4/4 = -B/A
(3/2)(-1/2) = C/A => -3/4 = C/A
As x = 0, y = 9 => C = 9
Hence, we get -3/4 = 9/-12 = C/A
C = 9 , A = -12
As A = -12, B = 12
Hence, the function required: -12x^2 + 12x + 9 = 0