Question

help me please!!
write the equation of each parabola in vertex form. the two points i am given is (0,9) & (2,1)

Answer 1

here is the graph

Answer 2

The very first thing I notice in your graph is the the point (2,1) represents the vertex of the parabola, and the other point, (0,9), the vertical intercept.

The simplest form of the equation of a vertical parabola is y=x^2. This parabola has its vertex at (0,0).

If we move the whole graph 2 units to the right, the vertex is now at (2,0), but the shape is exactly the same as before. The equation is y=a(x-2)^2.

If we move the whole graph both 2 units to the right and 1 unit up, the vertex is now at (2,1), but the shape is exactly the same as before. The equation is y-1=a(x-2)^2. This is our immediate situation.

We know that the graph goes through (0,9). Substitute x=0 and y=9 into the most recent equation, above, determine the value of a, and then write the equation again, including that "a" value.

Answer 3

ok so would the equation be 9-1=a(0-2)^2

Answer 4

and would it be a=2

Answer 5

@mathmale

Answer 6

Saige: 9-1=a(0-2)^2 simplifies to 8=a(-2)^2. Mind solving that for a?

Answer 7

well it would be a4 so wouldn't you divide both sides by 4 to get a=2

Answer 8

What I'd like to do here is to ask you to check whether this a=2 is correct or not.

First, write out the solution you've already proposed, with a = 2: y=2(x-2)^2+1.
Now substitute x=0. You should get 9. Do you?
Now substitute x = 2. You should get 1. Do you?
You should know by then whether or not your a =2 is correct. Good going.

Answer 9

yes you get 9 ans 1. so a=2 is correct

Answer 10

Perfect. Congrats. Any questions about this process?

Answer 11

no i get that part know i just dont get how to put it all i vertex form

Answer 12

In general, the equation of a parabola with vertex at (a,b) is y=a(x-1) + b. Some people might write it as y-b=a(x-a)^2. I thought it'd be a bit more helpful to show you how moving the vertex affects the equation y=ax^2.

Answer 13

Please explain in a bit more detail what you mean by "put it all in vertex form."

Answer 14

i need to put the graph that i attached in vertex form. i do not know how

Answer 15

Oh, I see. Actually, we've already done that.
What is the vertex as shown in the graph?
What is the one other point on that graph?

Answer 16

the vertex was (2,1) and the other point was (0,9)

Answer 17

so is the vertex form the equation y=2(x-2)^2+1.

Answer 18

That's right. As I mentioned a moment back, the general form for the equation of a parabola with vertex at (a,b) is y=a(x-a)^2 + b.
You correctly identified the v ertex from the graph, so you know that a=2 and b=1.
Substitute those two values into the general form. What do you get?

Answer 19

Excuse me, you've already done everything you needed to do. How satisfied are you that you understand what to do next time?

Answer 20

i understand how to do it all now. thank you so much. thanks for your time.

Answer 21

My great pleasure, Saige! See you.