Home > Algebra > Write an Equation Given Two Points

What is the equation of the parabola that has a vertex at # (-8, 5) # and passes through point # (2,27) #?

Answer 1

#(x--8)^2=+(50/11)(y-5)" "#Vertex Form

From the given: Vertex (-8, 5) and passing thru (2, 27), the parabola opens upward. The reason is that the vertex is lower than the given point.

By the vertex form , we can solve for the value of #p#

#(x-h)^2=+4p(y-k)#

#(2--8)^2=+4p(27-5)#

#10^2=4p(22)#

#100=4(22)p#

#25=22p#

#p=25/22#

Go back to the vertex form

#(x--8)^2=+4(25/22)(y-5)#

#(x--8)^2=+2(25/11)(y-5)#

#(x--8)^2=+(50/11)(y-5)" "#Vertex Form

graph{(x--8)^2=(50/11)(y-5)[-50,50,-25,25]}

God bless....I hope the explanation is useful.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Savannah Anderson

The equation of the parabola is ( y = \frac{1}{15}(x + 8)^2 + 5 ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.