What is the equation of the parabola that has a vertex at (5, 4) (5,4) and passes through point (7,-8) (7,−8)?

2 Answers
Binayaka C.
Oct 9, 2017

The equation of parabola is y = -3x^2+30x-71 y=−3x2+30x−71

Explanation:

The equation of parabola in vertex form is y= a(x-h)^2+ky=a(x−h)2+k

(h,k)(h,k) being vertex here h=5 , k=4 :. Equation of parabola in

vertex form is y= a(x-5)^2+4 . The parabola passes through

point (7 ,-8) . So the point (7 ,-8) will satisfy the equation .

:. -8 = a( 7-5)^2 +4 or -8 = 4a +4 or

4a = -8-4 or a = -12/4= -3 Hence the equation of

parabola is y= -3(x-5)^2+4 or

y= -3(x^2-10x+25)+4 or y = -3x^2+30x-75+4 or

y = -3x^2+30x-71

graph{-3x^2+30x-71 [-20, 20, -10, 10]}

Jim G.
Oct 9, 2017

y=-3x^2+30x-71

Explanation:

"the equation of a parabola in "color(blue)"vertex form" is.

color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))

"where "(h,k)" are the coordinates of the vertex and a"
"is a multiplier"

"here "(h,k)=(5,4)

rArry=a(x-5)^2+4

"to find a substitute "(7,-8)" into the equation"

-8=4a+4rArra=-3

rArry=-3(x-5)^2+4larrcolor(red)" in vertex form"

"distributing and simplifying gives"

y=-3(x^2-10x+25)+4

color(white)(y)=-3x^2+30x-75+4

rArry=-3x^2+30x-71larrcolor(red)" in standard form"

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