MATH SOLVE

4 months ago

Q:
# Write the equation of the parabola that has the vertex at point (2,7) and passes through the point (−1,3).

Accepted Solution

A:

Step One

Use the vertex to determine the basic equation for the parabola.

y = a(x - 2)^2 + 7 Notice the sign change for x. I have provided a graph to show how this would look with a = 1 (in red.)

What it means is the 2 has to be minus in order that the vertex will shift 2 units in the x direction.

Step Two

Use the point to solve for a.

y = a(x - 2)^2 + 7

When x = - 1

Then y = 3

3 = a(-1 - 2)^2 + 7 combine -1 with - 2

3 = a (-3)^2 + 7

3 = 9a + 7 Subtract 7 from both sides

3 - 7 = 9a

-4 = 9a Divide by 9.

a = -4/9

or

a = - 0.4444

y = -0.4444(x + 2)^2 + 7 <<<<< answer

y = - 4/9 (x + 2)^2 + 7

Note: if you have choices, list them please.

Note: The red graph is y = (x - 2)^2 + 7 ; a = 1

The blue graph is y = - 4/9(x - 2)^2 + 7 ; a = - 0.44444

You should notice that the a does 3 things to the graph. Before you read the answer, what are those three things? The answer is in the comments.

Use the vertex to determine the basic equation for the parabola.

y = a(x - 2)^2 + 7 Notice the sign change for x. I have provided a graph to show how this would look with a = 1 (in red.)

What it means is the 2 has to be minus in order that the vertex will shift 2 units in the x direction.

Step Two

Use the point to solve for a.

y = a(x - 2)^2 + 7

When x = - 1

Then y = 3

3 = a(-1 - 2)^2 + 7 combine -1 with - 2

3 = a (-3)^2 + 7

3 = 9a + 7 Subtract 7 from both sides

3 - 7 = 9a

-4 = 9a Divide by 9.

a = -4/9

or

a = - 0.4444

y = -0.4444(x + 2)^2 + 7 <<<<< answer

y = - 4/9 (x + 2)^2 + 7

Note: if you have choices, list them please.

Note: The red graph is y = (x - 2)^2 + 7 ; a = 1

The blue graph is y = - 4/9(x - 2)^2 + 7 ; a = - 0.44444

You should notice that the a does 3 things to the graph. Before you read the answer, what are those three things? The answer is in the comments.