# 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

#### 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]}