how to create a quadratic function with two zeros

Question

anonymous · Answer

anyone?

anonymous · Answer

@IMStuck

mathstudent55 · Answer

Choose any two zeros.
Show them.

mathstudent55 · Answer

@lexicampion36 
Are you there?

anonymous · Answer

what are two zeros? @mathstudent55

mathstudent55 · Answer

The points where the graph of the function crosses the x-axis.
When you solve a quadratic function, the zeros are the solutions.

anonymous · Answer

-7 and 5

mathstudent55 · Answer

Ok. We'll use your numbers very soon. Let me just explain what we are doing with an example.

Let's say you are given this quadratic equation to solve by factoring:

$x^2 + 3x + 2 = 0$

anonymous · Answer

ok

mathstudent55 · Answer

You factor the left side:

$(x + 1)(x + 2) = 0$

Set both factors equal to zero and solve each equation.

$x + 1 = 0$ or $ x + 2 = 0$

x = -1 or x = -2

Ok?

anonymous · Answer

ok i got that

mathstudent55 · Answer

Ok. You see that if you have a quadratic equation that can be factored, you can factor it and arrive at a solution.

Now we are going to work backwards.
We have the solutions you came up with, and we want to know which equation has those solutions.

anonymous · Answer

(x+5)(x-7)=y

mathstudent55 · Answer

We take your two solutions (also called zeros), and this is what we do.

mathstudent55 · Answer

Close but there is a little problem with your equation.

anonymous · Answer

oh it has to be opposite so (x-5)(x+7)=y

mathstudent55 · Answer

First, I think you meant for it to be equal to zero.
(x+5)(x-7)=0

anonymous · Answer

oh right

mathstudent55 · Answer

Second (I see you figured it out), it has to be
(x + 7)(x - 5) = 0

mathstudent55 · Answer

The rule is if you have zeros k1, k2, k3, etc., then each binomial is x - k1, x - k2, x - k3, etc.

anonymous · Answer

ok i got that then you factor it out? so its now 
x(x+7)-5(x-7)

anonymous · Answer

so x^2-2x-35?

mathstudent55 · Answer

In your case you chose zeros -7 and 5, so the binomials 
are
x - (-7) = x + 7
x - 5 = x - 5

Now the equation is the product of the binomials equaling zero.

(x + 7)(x - 5) = 0

Use FOIL to multiply out the left side.

anonymous · Answer

whats FOIL?

mathstudent55 · Answer

x^2 - 5x + 7x -35 = 0

x^2 + 2x - 35 = 0 is the quadratic equation with zeros -7 and 5.

anonymous · Answer

yay!!! i got right! thank you for your help in understanding.

anonymous · Answer

i have one more for you haha hold on.

mathstudent55 · Answer

FOIL is a way of remembering how to multiply together two binomials.

mathstudent55 · Answer

|dw:1407100193819:dw|