# How do you write the equation of the parabola in vertex form given vertex (4,-1) and y intercept (0,15)?

##### 2 Answers

See below.

#### Explanation:

Equation in vertex form is

In this example

So

Hence:

Solving for

#### 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 constant.

#"here " (h,k)=(4,-1)#

#rArry=a(x-4)^2-1#

#"to find a substitute "(0,15)" into the equation"#

#15=16a-1rArra=1#

#rArry=(x-4)^2-1larrcolor(red)" in vertex form"#

graph{(x-4)^2-1 [-10, 10, -5, 5]}