write the equation of each parabola in vertex form

Question

vertex(-3,7); point (-2,-5)

Answer 1

Hi Keithen,

Problem: write the equation of each parabola in vertex form vertex(-3,7); point (-2,-5)

Given: vertex(-3,7); point (-2,-5)

Find Parabola in Vertex Form

The Vertex form of the parabola is y = a(x-h)² + k

Where the vertex is (h,k)

The amplitude is a

1) Substitute the vertex values into the equation (-3,7) h=-3, k=7

y=a (x-(-3))² +7

y=a (x+3)² +7

2) Use the point given to determine the value of a Point =(-2, -5)

-5 = a (-2+3)² +7

-12 = a (1)

-12 = a

3) Now you have the values and can write your equation.

y = -12 (x+3)² +7

To Check if this equation is correct, use the point you were given (-2, -5) substitute the x value into the equation and determine the value of y is should be -5

y= -12 (-2 +3)² +7

y= -12 + 7 = -5

It's correct!!

Hope this helps :)

Let me know if you have more questions.