Share

## STEM: If you can rewrite a quadratic equation as a product of factors that equals zero, you can solve the equation. To sol

Question

STEM:

If you can rewrite a quadratic equation as a product of factors that equals zero, you

can solve the equation. To solve equations in this manner, you must use all your

factoring skills.

Example:

What are the solutions of the equation x2– x = 20?

First rewrite the equation so that one side equals zero.

x2– x = 20

x2 – x – 20 = 20 – 20

x2 – x – 20 = 0

Subtract 20 from each side.

Simplify.

Now, factor to rewrite the equation as a product of factors equal to zero. Find two

integers whose product is –20 and whose sum is –1. The product of 4 and –5 is

–20, and the sum of 4 and –5 is –1.

x + 4 = 0

x + 4 – 4 = 0 – 4

x = –4

x2 – x – 20 = 0

(x + 4)(x – 5) = 0

or

or

or

x – 5 = 0

x – 5 +5 = 0 +5

x = 5

The solutions are –4 and 5.

These “solutions” tell us where our quadratic function passess through the x-axis (ie this tells us the “roots” aka “x -intercepts” aka “zeros” aka “solutions” aka “zeros” are)

Question:

In the graph provided in the example, what do the coordinates (-4,0) and (5,0) represent?

A

The y- intercept of the function (ie where the function passes through the y-axis)

B

The x-intercept of the function (ie where the function passes through the x-axis)

C

The vertex of the function

D

none of the above

E

the zeros of the quadratic function

F

the roots of the quadratic function

in progress
0

Mathematics
6 months
2021-08-24T21:56:07+00:00
2021-08-24T21:56:07+00:00 1 Answers
4 views
0
## Answers ( )

9514 1404 393

Answer:A, E, F

Step-by-step explanation:Every point on the graph has coordinates (x, f(x)). This means a point such as (-4, 0) or (5, 0) is a point on the x-axis where f(x) = 0. It is all of …

These terms are used essentially interchangeably.