# How do you write the quadratic equation given Vertex: (3,-11) Passing though: (5,2)?

##### 1 Answer

Feb 19, 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) is the vertex and a, a constant.

#"here " (h,k)=(3,-11)#

#rArry=a(x-3)^2-11" is the partial equation"# To find a, substitute the point (5 ,2) into the equation.

#2=a(5-3)^2-11#

#rArr2=4a-11#

#rArra=(2+11)/4=13/4#

#rArry=13/4(x-3)^2-11larrcolor(red)" in vertex form"# distributing and simplifying gives.

#y=13/4x^2-39/2x+73/4larrcolor(red)" in standard form"#