MATH SOLVE

4 months ago

Q:
# PLEASE HELP ME!!! HIGHSCHOOL MATH!!!Write the equation of the parabola when the vertex is (0,5) and it passes through (2,9)

Accepted Solution

A:

we know that

the equation of a vertical parabola in vertex form

y=a*(x-h)²+k

(h,k)------> (0,5)

y=a*(x-0)²+5

y=a*x²+5

substitute the point (2,9) in the equation

9=a*(2)²+5------> 9=4*a+5-------> 4*a=9-5-----> 4*a=4-----> a=1

the equation of the vertical parabola is

y=x²+5

the equation of a horizontal parabola in vertex form

x=a*(y-k)²+h

(h,k)------> (0,5)

x=a*(y-5)²+0

x=a*(y-5)²

substitute the point (2,9) in the equation

2=a*(9-5)²------> 2=16*a------> a=1/8

the equation of the horizontal parabola is

x=(1/8)*(y-5)²

the answer is

the equation of the vertical parabola is y=x²+5

the equation of the horizontal parabola is x=(1/8)*(y-5)²

see the attached figure

the equation of a vertical parabola in vertex form

y=a*(x-h)²+k

(h,k)------> (0,5)

y=a*(x-0)²+5

y=a*x²+5

substitute the point (2,9) in the equation

9=a*(2)²+5------> 9=4*a+5-------> 4*a=9-5-----> 4*a=4-----> a=1

the equation of the vertical parabola is

y=x²+5

the equation of a horizontal parabola in vertex form

x=a*(y-k)²+h

(h,k)------> (0,5)

x=a*(y-5)²+0

x=a*(y-5)²

substitute the point (2,9) in the equation

2=a*(9-5)²------> 2=16*a------> a=1/8

the equation of the horizontal parabola is

x=(1/8)*(y-5)²

the answer is

the equation of the vertical parabola is y=x²+5

the equation of the horizontal parabola is x=(1/8)*(y-5)²

see the attached figure