How to determine the rule of a parabola?

enter image source here
Can someone please explain to me how to do question 3? Thank!

1 Answer
Dec 8, 2017

y=3/2x^2+6x+10

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 turning point"
"and a is a multiplier"

"here "(h,k)=(-2,4)

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

"to find a substitute "(4,58)" into the equation"

58=a(6)^2+4rArra=54/36=3/2

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

"expanding and simplifying gives"

y=3/2(x^2+4x+4)+4

rArry=3/2x^2+6x+10larrcolor(red)"in standard form"