Home > Algebra > Vertex Form of a Quadratic Equation

What is the vertex form of #y=-x^2-5x-19#?

Answer 1

Ethan Adkins

#y=-(x+5/2)^2-51/4#

#y=-x^2-5x-19#

Factor out a -1.

#y=color(red)(-)(x^2color(red)+5xcolor(red)+19)#

Add and subtract #(5/2)^2# within the grouping.

#y=-(x^2+5xcolor(red)(+25/4)+19color(red)(-25/4))#

Factor the first 3 terms of the right hand side.

#y=-[color(red)((x+5/2)^2)+19-25/4]#

Simplify.

#y=-[(x+5/2)^2+color(red)(51/4)]#

#y=color(red)-(x+5/2)^2color(red)-51/4#

graph{-x^2-5x-19 [-5, 1, -20, -10]}

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

Answer 2

Kennedy Adams

The vertex form of the quadratic equation ( y = -x^2 - 5x - 19 ) is ( y = -(x + \frac{5}{2})^2 - \frac{71}{4} ).

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.