Question

Graph the function, then answer the questions about the graph. (please show work and explain!!! thanks!)

y=1/2x^2-x-6

Vertex:________
x-intercepts:_________
y-intercept:_________
***and GRAPH!! :D
thanks!! :)

Answer 1

4 parts:
1, find the vertex
2, find the x-int.
3, find the y-int.
4. GRAPH The equation!! :D

Answer 2

(1/2x^2)-x-6?

Answer 3

first identify a, b, and c

Answer 4

a=1/2
b=-1
c=-6
???

Answer 5

good

Answer 6

if we have an equation in standard form y = ax^2+bx+c, we can easily spot the y-intercept

Answer 7

plug in x = 0 to get

y = ax^2+bx+c

y = a(0)^2+b(0)+c

y = 0a + 0b + c

y = c

So when x = 0, y = c

This means that the y-intercept for y = ax^2+bx+c is the point (0, c)

Answer 8

So that part is relatively easy (compared to the other parts)

Answer 9

so what?? y-intercept is (0,-6) ??

Answer 10

yes, you replace c with -6

Answer 11

how do i find the other stuff tho?

Answer 12

The steps I showed were in general. So if you see y = ax^2+bx+c, you can jump to the y-intercept of (0, c)

This means that if you see y = 1/2x - x - 6, you can jump to the y-intercept of (0, -6) quickly

Answer 13

oh okay i see :) what about x-int? how do i find that for my problem?

Answer 14

Do you remember how to find the vertex?

Answer 15

To find the x-intercepts, plug in y = 0 and solve for x

Answer 16

(h,k)=vertex right?

Answer 17

yes

Answer 18

how am i finding the x-intercepts??

Answer 19

can u pls show me?? I'm a little confused :(

Answer 20

Finding x-intercepts. Plug in y = 0 and solve for x

y=1/2x^2-x-6

0=1/2x^2-x-6

2*0 = 2*1/2x^2 - 2*1x - 2*6

0 = x^2 - 2x - 12

x^2 - 2x - 12 = 0

Answer 21

Now solve x^2 - 2x - 12 = 0 for x

Answer 22

so a=1
b=-2
c=-12
?? what do i do with that?

Answer 23

plug them into the quadratic formula

Answer 24

\[\Large x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\]