Question

Determine the 2 x-intercepts and the vertex of a parabola in (x,y) form and how you found these ordered pairs in a sentence. (-1,0) (2,0)

Answer 1

I am not clear on the question. Also, what is the equation?

Answer 2

the first question was to find the corresponding y values when x= -2,-1,0,1,2,3 for the equation y=x^2-x-2

Answer 3

i got (-2,4) (-1,0) (0,-2) (1,-2) (2,0) and (3,4)

Answer 4

To find x-intercepts, Let y = 0 and solve for x. So:
\[y=x^2-x-2 \rightarrow 0=x^2-x-2\]
Now you have to factor to solve. (Or quadratic equation)
You will get 2 solutions and they want you to write it in (x, y) form. Since you let y=0, both will have 0 for y.

Answer 5

for the vertex, you use that -b/2a again to find the x-coordinate and then plug it in to find the y-coordinate - like the last problem

Answer 6

so (x-1)(x+2)

Answer 7

and the vertex would be -1/2

Answer 8

You are close. \[\left( x-1 \right)\left( x+2 \right)=x ^{2}+x-2\] but you want \[x ^{2}-x-2\] so your signs are off.

Answer 9

so it would be (x-1)(x-2)

Answer 10

no (x+1)(x-2)

Answer 11

You were right that you needed opposite signs

Answer 12

yes ... now set each factor = 0 and solve each equation.

Answer 13

but when I graph my (x,y) from the first question. the graph shows the x-intercepts as (-1,0) (2,0)

Answer 14

when you set x + 1 = 0 and solve,
- 1 - 1
We get: x = 0

Answer 15

What do you get when you set x - 2 = 0?

Answer 16

-2

Answer 17

Yes. Now remember you set y = 0 and solved for x, so the points you found are (1, 0) and (-2, 0)

Answer 18

Now, back to the vertex. When you set x = -b/2a, you found the x-coordinate of the vertex to be 1/2. What is the y-coordinate?

Answer 19

1.25

Answer 20

\[y=x ^{2}-x-2\] so \[y=\left( \frac{ 1 }{ 2 } \right)^{2}-\frac{ 1 }{ 2 }-2\]

Answer 21

I think maybe you made a sign error. \[\left( \frac{ 1 }{ 2 } \right)^{2}=\frac{ 1 }{ 4 }\]

Answer 22

so: \[\frac{ 1 }{ 4 }-\frac{ 1 }{ 2 }-2 = ?\]

Answer 23

i got -1/2 for my vertex

Answer 24

only for the x-coordinate. The vertex is a point. You need the y-coordinate. You have to replace x with 1/2 to find the corresponding y.

Answer 25

Try this. 1/4 = 0.25 and 1/2 = 0.5, so we have 0.25-0.5-2

Answer 26

-2.25

Answer 27

yes! Or - 2 1/4

Answer 28

Now express it as a point, so (1/2, -2.25)

Answer 29

And it sounded like they want you to explain in words what you did.

Answer 30

In case it might be useful to you later, this is a list of my videos for factoring and solving quadratic equations by factoring:
www.mathmods.com/mat100/Chapters/Factoring/factoring_video_links.pdf

Answer 31

@davisla I am still having trouble with this problem. I figured out the factoring and the vertex but when I graph this from the first part the x-intercepts that I get from graphing are (-1,0) (2,0). Can you please help me?

Answer 32

I will make you a video of the whole problem in about 15 min if that is ok

Answer 33

yes thank you

Answer 34

here is the video ... let me know if this doesn't do it for you:
www.mathmods.com/Math_Tutoring/vertex_int_parabola_5_5_min/vertex_int_parabola_5_5_min.html

Answer 35

Sorry, I didn't read your question correctly ... here is the graph:
www.mathmods.com/Math_Tutoring/vertex_int_parabola_1_min/vertex_int_parabola_1_min.html