# How do you write a quadratic equation with vertex (2,1) y intercept (0,-3)?

##### 1 Answer

Apr 20, 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 constant.

#"here " (h,k)=(2,1)#

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

#"to find a, substitute " (0,-3)" into the equation"#

#-3=4a+1#

#rArr4a=-4rArra=-1#

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

#"distributing and simplifying gives"#

#y=-(x^2-4x+4)+1#

#color(white)(y)=-x^2+4x-4+1#

#rArry=-x^2+4x-3larrcolor(red)" in standard form"#

graph{-x^2+4x-3 [-10, 10, -5, 5]}