Question

Help and check my work.. Quadratic Function.

Answer 1

f(x)=-x^2 -2x+10
a=-1
b=-2

Vertex (-1,13)

It says my wrong and that the vertex is (-1,11)

Answer 2

@freckles

Answer 3

so you found the x-coordinate of the vertex is -1

Answer 4

now f(x)=-x^2-2x+10
replace x with -1
f(-1)=-(-1)^2-2(-1)+10

Answer 5

should get -1+2+10

Answer 6

-.- I missed the front negative.. Thanks

Answer 7

Can you help with a few more?

Answer 8

f(x)=2(x+3)^2 -4

Answer 9

a=2
h=-3
k=-4

Vertex- (-3,-4)

y-intercept is 14
axis of symmetry- -3

0=2(x+3)^2 -4
4=2(x+3)^2

2=(x+3)^2
square root 2 = square root (x+3)^2

Answer 10

axis of symmetry should be an equation
x=-3

Answer 11

Yes.

Answer 12

what are you doing at the end there?
Trying to solve for x when y is 0?

Answer 13

aka finding x-intercepts

Answer 14

Yes im trying to find x-intercepts. I have to graph this problem

Answer 15

\[2=(x+3)^2 \\ \pm \sqrt{2}=x+3\]
one more step and you have it

Answer 16

-3+- square root 2=x

x= -1.58
x=-4.41

Answer 17

-3+sqrt(2) is -1.59
-3-sqrt(2) is right

Answer 18

and when I say is I mean approximately because we did just round these numbers :p

Answer 19

How am I suppose to graph this?

Answer 20

I would plot the x and y-intercepts first

Answer 21

find 14 on the y-axis

Answer 22

find -1.59 and -4.41 on the x-axis

Answer 23

and then plot the vertex

Answer 24

connect dots after that

Answer 25

Its an online system. I only have 2 dots to use. I guess the vertex and the y-intercept.

Answer 26

That worked.

Answer 27

cool stuff

Answer 28

getting a drink of water brb for 1 question if you have it

Answer 29

k back

Answer 30

Okay.. The next problem im stuck on..

f(x)=x^2+3x-4

Answer 31

still graphing?

Answer 32

Yes

Answer 33

so as we seen with previous we only need y-intercept and vertex for your online system thingy

Answer 34

y-intercept
you set x to 0 and you get y is?

Answer 35

that part is easy
so I will go ahead and ask you about the x-coordinate of the vertex
vertex has x-coordinate -b/(2a)

Answer 36

I got (-1.5,1.75)

Answer 37

let me check

Answer 38

\[a=1,b=3,c=-4 \\ \frac{-b}{2a}=\frac{-3}{2(1)}=-1.5 \text{ good }\]

Answer 39

\[f(\frac{-3}{2})=(\frac{-3}{2})^2+3(\frac{-3}{2})-4 \\ =\frac{9}{4}-\frac{9}{2}-4 ...\]

Answer 40

\[=\frac{9}{4}-\frac{18}{4}-\frac{16}{4}=\frac{9-18-16}{4}=\frac{9-34}{4}=\frac{-25}{4}\]

Answer 41

hmmm...let me check my arithmetic because we got different y-coordinates

Answer 42

I plugged in -1.5 not the fraction

Answer 43

well it shouldn't matter
-1.5 is the same as -3/2

Answer 44

so you did (-1.5)^2+3(-1.5)-4

Answer 45

I made an error. I got -6.25

Answer 46

awesome stuff

Answer 47

-25/4 is the same as -6.25

Answer 48

Yep..
y-intercept is -4

Answer 49

that is correct
so you have to plot (-1.5,-6.25) and (0,-4)

Answer 50

I have to solve for the rest.. axis of symmetry, x-intercepts, domain, range

Answer 51

well you already have axis of symmetry really

Answer 52

the answer is in the vertex

Answer 53

x=?

Answer 54

this question I was say is a bit easier than last in finding x-intercepts
since x^2+3x-4 is factorable

Answer 55

domain for all polynomial functions y=f(x) is all real numbers

the range though is not as easy to say about polynomials
since you had to graph your parabola look at the graph and see what y values got hit by the function

Answer 56

Range- [-4,infinity sign)

Answer 57

use your y-coordinate from your vertex
this y should be the lowest of all y's you could possibly choose that will get hit
should be lower than the y-intercept you found also