# How do you write the quadratic equation given Vertex: (1/2, 1/2) Passing though: (3/4, 1/4)?

##### 1 Answer

Sep 4, 2017

#### Explanation:

#"the equation of a quadratic 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)=(1/2,1/2)#

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

#"to find a substitute "(3/4,1/4)" into the equation"#

#1/4=1/16a+1/2rArra=-4#

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

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