118k views
2 votes
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

User Berker
by
8.5k points

2 Answers

9 votes

Answer:

The x-intercepts are happen are when y = 0. If you tried to substitute y = 0 into a quadratic in the standard form you can not use traditional methods for solving for x.

Y=0 when looking for an x-intercept. Doing the factored form you are finding the x-intercepts. You always want the equation to equal 0 then factor out the equation till you get the numbers for the x-intercept.

User Jldupont
by
8.0k points
4 votes

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.

User Tyneequa
by
7.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories