# What is the vertex form of #4y=5x^2 -7x +3#?

##### 2 Answers

#### Explanation:

Remember that the **vertex form** (our target) is in general

Given

We will need to divide everything by

We can now extract the

We want to write

Remember that the squared binomial

since the coefficient of the

our value for

So we need to insert a term of

...but remember that this factor is multiplied by

so to balance thing out we will need to subtract

Our equation now looks like

Writing this with a squared binomial and simplifying the constant terms:

which is our required vertex form with vertex at

For verification purposes here is a graph of the original equation:

#### 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"#

#"to express "5x^2-7x+3" in this form"#

#"use the method of "color(blue)"completing the square"#

#• "the coefficient of the "x^2" term must be 1"#

#rArr5(x^2-7/5x+3/5)#

#• " add/subtract "(1/2"coefficient of x-term")^2" to"#

#x^2-7/5x#

#5(x^2+2(-7/10)xcolor(red)(+49/100)color(red)(-49/100)+3/5)#

#=5(x-7/10)^2+5(-49/100+3/5)#

#=5(x-7/10)^2+11/20#

#rArr4y=5(x-7/10)^2+11/20#

#rArry=1/4[5(x-7/10)^2+11/20]#

#color(white)(rArry)=5/4(x-7/10)^2+11/80#