Answer:
f(x) = -4/3x² -2/3x +10
Step-by-step explanation:
The quadratic regression function of a graphing calculator or spreadsheet can determine the equation for you.
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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
-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).
