Home > Algebra > Vertex Form of a Quadratic Equation

What is the vertex form of #y= 3x^2-30x-72 #?

Answer 1

Abigail Allen

#y=3(x-5)^2 -147#

Given:#" "y=3x^2-30x-72#

Let #k# be the correction canstant

Write as;#" "y=3(x^(color(magenta)(2))-30/3x)-72+k#

Move the power of #color(magenta)(2)# to outside the bracket

#y=3(x-30/3color(green)(x))^(color(magenta)(2))-72+k#

Remove the #color(green)(x)# from #30/3x#

#y=3(x-30/3)^2 -72+k#

Apply #1/2xx(-30/3) = 30/6 = 5#

#y=3(x-5)^2 -72+k#

It must be the case for the correction to be effective that

#color(red)(3)xx(-5)^2+k=0" "=>" "k=-75#

#color(red)("(do not forget to multiply by the value outside the brackets)")#

#y=3(x-5)^2 -72-75#

#y=3(x-5)^2 -147#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.