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

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