How do i write equations when I am given a graph of a parabola?

Question

I am stuck!
I have to write an equation in the form y=a(x-h)^2+k
I am given two points:
The vertex (1,3)
and another point (3,11)
If anyone could please explain this to me step by step that would be WONDERFUL, and I could finish the rest of my homework. :''[

THANK YOU BOTH SOOOO MUCH!
My teacher isn't very good at explanations.-___-'
Thank you!

Answer 1

Remember that in a parabola expressed in this form the variables h and k represent the coordinates of the vertex of the equation. Since you are given the vertex (1, 3), then h = 1 and k = 3.

The object here is to solve for "a" so you can write the entire equation. Since you are given a point, (3,11), which also lies on the parabola, you can do that by plugging these values directly into the equation of the parabola.

11 = a(3 - 1)² + 3
11 = a(2)² + 3
11 = 4a + 3
11 - 3 = 4a
8 = 4a
2 = a

Since "a" is positive, then this parabola opens upward. Its final form is:

y = 2(x - 1)² + 3.

Answer 2

The vertex is (h, k). So, h=1 and k=3. You can substitute these values into your equation. It should look like the following:

y=a(x-1)^2 + 3

From there, you have to substitute the point on the graph for x and y in the equation, like this:

11=a(3-1)^2 + 3

To simplify this and solve for a, first you want to do the math in the parentheses:

3-1 = 2
11=a(2)^2 + 3

You're next step would be to square 2...2 x 2 = 4. Therefore, your equation should now look like the following:

11=4a + 3

Subtract 3 from both sides. This will cancel out the 3 on the right because 3-3=0.

11-3 = 4a + 3 -3
11-3 = 4a

11-3=8. So, you now have:
8=4a

From here, you want to divide both sides by 4 which will cancel out the 4 because a number over itself is always equal to one.

8/4 = a
or a = 2

I hope this is helpful! Good luck with your homework!

Answer 3

Hello :-)

You are given the vertex, and it is usually expressed as (h,k).

This means (h,k) is (1,3).

h = 1
k = 3

Since you have both h and k already, substitute the data given by the other point (3, 11) as (x, y), temporarily, to get a.

Thus,

11 = a (3 -1)^2 + 3

11 = a (2)^2 + 3
11 = a (4) + 3
8 = 4a
a = 2.

The equation is thus:

y = 2 (x-1)^2 + 3

You should check if this is correct by substituting the points given.

Answer 4

once you're given the graph of a parabola, locate this techniques: The vertex - call this (h,ok) The direction of beginning off - regardless of if this is up, a>0; regardless of if this is down, a<0 The width- If narrower than x^2, a>one million; regardless of if this is wider, 0