Question

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?

Answer 1

`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]}