Question

how to create a quadratic function with two zeros

Answer 1

anyone?

Answer 2

@IMStuck

Answer 3

Choose any two zeros.
Show them.

Answer 4

@lexicampion36
Are you there?

Answer 5

what are two zeros? @mathstudent55

Answer 6

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

Answer 7

-7 and 5

Answer 8

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:

\(x^2 + 3x + 2 = 0\)

Answer 9

ok

Answer 10

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?

Answer 11

ok i got that

Answer 12

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.

Answer 13

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

Answer 14

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

Answer 15

Close but there is a little problem with your equation.

Answer 16

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

Answer 17

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

Answer 18

oh right

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

so x^2-2x-35?

Answer 23

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.

Answer 24

whats FOIL?

Answer 25

x^2 - 5x + 7x -35 = 0

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

Answer 26

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

Answer 27

i have one more for you haha hold on.

Answer 28

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