Question

Explain relationship between the factors of a quadratic expression, the roots of the related quadratic equation, and the x-intercepts if the graph of the related function

Answer 1

Step-by-step explanation:

So, let's use x2 - 3x - 28 as an example.

 

It's factors are (x - 7)(x + 4).

 

The roots are the x-values that make our expression equal 0. In order for x2 - 3x - 28 to equal 0, either of our factors need to equal 0, since 0 times anything is 0.

 

x2 - 3x - 28 = 0

(x - 7)(x + 4) = 0

 

x - 7 = 0

x = 7

(7 - 7)(7 + 4) = 0(11) = 0

 

x + 4 = 0

x = -4

(-4 - 7)(-4 + 4) = -11(0) = 0

 

That gives us two points on our graph, (7,0) and (-4,0). Where are those? On the x-axis! Thus, there are our x-intercepts.

 

By the way, for the future, along the x-axis, y = 0, so if you are asked for the x-intercepts (or roots), set y = 0 and solve for x.

 

Along the y-axis, x = 0, so if you are asked for the y-intercepts, set x = 0 and solve for y.

 

y = 02 - 3(0) - 28

y = -28

 

So, the y-intercept(s) of our same equation is y = -28, or (0,-28).

 

Boom.