ShmoopTube

00:02

Okay sy match members Next up Another quadratic word problem

00:06

for you Which of the following points is a location

00:08

where the function f of x equals negative to x

00:10

squared Plus twelve ax plus fifty four crosses the horizontal

00:14

axis Okay well why did the chicken cross the road

00:21

Who knows The chicken Probably doesn't It just does what

00:23

it wants A good thing We do know why the

00:25

function crossed the horizontal axis It was equal to zero

00:29

c that's the horizontal axis there That ex thing we

00:32

want to find the values of x that make f

00:34

of x equals zero So we need to solve the

00:37

if equation zero equals negative to x squared plus twelve

00:40

ax plus fifty for so basically a factoring question We

00:43

feel queasy when the coefficient of x squared isn't equal

00:46

toe one So the first step is to factor out

00:49

negative two from the right side of the equation Then

00:51

we got zero equals negative two times quantity x squared

00:55

among six x there minus twenty seven Right now we

00:58

gotta factor the quadratic inside the parentheses We got two

01:01

factors of negative twenty seven So what are they What

01:05

times What is twenty seventy s One in twenty seven

01:08

Morning Look in the back row There What else Times

01:10

What is twenty seven Yeah nine and three nine times

01:13

Three is twenty seven and we know that we've got

01:16

to get a negative six year so we're going to

01:17

do the negative sign on the nine and the positive

01:21

sign on the three because negative nine and three is

01:23

that negative six So that works on the negative six

01:25

x thingy there and we gotta minus twenty seven We

01:28

all play that negative nine times three so that's what

01:30

it looks like we got zero equals negative two times

01:34

princess expose three and princes x minus nine right there

01:37

so we find a solution by setting the expressions inside

01:40

The princess is equal to zero in solving for acts

01:42

Well first if x plus three zero than x has

01:45

to be negative three and second of x minus nine

01:48

to zero the next has to be nine We'll fx

01:50

then crosses the horizontal axis at the point Negative three

01:54

zero and nine zero that's it So the answer is 00:01:58.455 --> [endTime] d we're done

Full Transcript