Using the vertex form, find a formula for the parabola with vertex (2,14) that passes through the point (1,7)?

7=a(1-2)^2+14
so I got a to be -7

so the answer should be y=-7(x-2)^2+14 but my online math hw says I'm not correct?

2 Answers
Nov 27, 2017

y=-7(x-2)^2+14 or x=-1/49(y-14)^2+2

Explanation:

There can be two parabolas with vertex at (2,14) and passing through (1,7).

One of the form (y-14)=a(x-2)^2 and other (x-2)=a(y-14)^2

Case 1 - If (y-14)=a(x-2)^2 passes through (1,7) then

7-14=a(1-2)^2 i.e. a=-7

and equation is (y-14)=-7(x-2)^2 i.e. y=-7(x-2)^2+14, a vertical parabola

Case 2 - If (x-2)=a(y-14)^2 passes through (1,7) then

1-2=a(7-14)^2 i.e. 49a=-1 i.e. a=-1/49

and equation is x-2=-1/49(y-14)^2 i.e. x=-1/49(y-14)^2+2, a horizontal parabola

graph{(y+7x^2-28x+14)(49x+y^2-28y+98)((x-1)^2+(y-7)^2-0.05)((x-2)^2+(y-14)^2-0.05)=0 [-10.21, 9.79, 4.52, 14.52]}

Nov 27, 2017

y=-7(x-2)^2+14
x=-1/49(y-14)^2+2

Explanation:

Given -

Vertex (2, 14)
Passes through point (1, 7)

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This parabola may be either open down or open to left.

The equation of the parabola that opens down.

y=a(x-h)+k

Where (h, k) is the vertex

y=a(x-2)^2+14

The parabola is passing through point (1,7)

Substitute this to find the value of a

a(1-2)^2+14=7
a+14 = 7

a=7-14=-7

Then the required equation is -

y=-7(x-2)^2+14

Parabola May open to left. Then the equation is -

x=a(y-k)^2+h

x=a(y-14)^2+2

a(y-14)^2+2=x

a(7-14)^2+2=1

49a+2=1

49a=1-2=-1

a=-1/49

Then the equation is -

x=-1/49(x-14)^2+2