SOLUTION: If the zeroes of a quadratic function are -4 and 6, and its y-intercept is 12, determine the function in general form without using regression. My name is Chantal and I know that

Question 187247: If the zeroes of a quadratic function are -4 and 6, and its y-intercept is 12, determine the function in general form without using regression.
My name is Chantal and I know that -4 and 6 are the roots and -12 is the last part of the equation in general form but I don't know what he means by regression. I'm not sure how to go about doing this equation. If you could help me it would be greatly appreciated. I missed school when we learnt this.This is not from a book.
Chantal Laroche
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"If the zeroes of a quadratic function are -4 and 6" means that the solutions to the equation are or (ie if you plug in or into , you will get zero)

or Start with the given solutions

or Get the terms to the left side (so the right side is zero)

Combine the equations using the zero product property

Note: the zero product property states that if then either or (or possibly both)

Place an additional variable "a" onto the front of the equation. Note: this will be needed to satisfy the third condition.

FOIL

Combine like terms.

So the equation that has the zeros of -4 and 6 is

Now there's an additional condition: The y-intercept is 12

This means that when ,

Start with the previous equation.

Plug in and

Square 0 to get 0

Multiply

Combine like terms.

Divide both sides by -24 to isolate "a".

Reduce

So the value of "a" is

This means that the equation then goes from to

Now distribute to get:

and multiply:

===========================================================

Answer:

So the equation with the zeros -4 and 6 with the y-intercept of 12 is:

Here's the graph to visually verify our answer:

Graph of with x-intercepts (-4,0) and (6,0) with the y-intercept (0,12)
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