How do you find the equation of the parabola with vertex (-3, 1) and passing thru (-5, -11) if its axis of symmetry is parallel to the Y-axis?

1 Answer
Oct 26, 2017

y=-3x^2-18x-26

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)=(-3,1)

rArry=a(x+3)^2+1

"to find a substitute "(-5,-11)" into the equation"

-11=4a+1rArr4a=-12rArra=-3

rArry=-3(x+3)^2+1larrcolor(red)" in vertex form"

"distributing and simplifying gives"

y=-3x^2-18x-26larrcolor(red)"in standard form"
graph{-3x^2-18x-26 [-11.25, 11.25, -5.625, 5.625]}