Question

The graph of a quadratic function has x intercepts at -3 and 5/2, and y intercept at 10. Give the function.

Answer 1

-2/3( 2x^2 + x - 15) is the answer.

From the given x-intercepts, 2 factors of the equation will be (x + 3) and

(2x - 5):- So we can write:

At the y-intercept x = 0 so we have the equation a(0+3)(2(0) - 5) = 10 where a is a constant.

a * -15 = 10

a = -2/3 so the function is (-2/3)(x + 3)(2x - 5)

= -2/3( 2x^2 + x - 15).

Answer 2

f(x) = -4/3x² -2/3x +10

Explanation:

The quadratic regression function of a graphing calculator or spreadsheet can determine the equation for you.

___

Or, you can determine it yourself.

The equation can be written in the form ...

f(x) = a(x +3)(x -5/2) . . . . . . . using the given x-intercepts

for some value of "a"

For x = 0, this must match the y-intercept.

f(0) = a(0 +3)(0 -5/2) = 10

-15/2·a = 10

a = -20/15 = -4/3

So, the function can be written as ...

f(x) = (-4/3)(x +3)(x -5/2)

or

f(x) = -4/3x² -2/3x +10