SOLUTION: Use completing the square to find the zeros of the function y=9x^2-12x-33.

Question 121503: Use completing the square to find the zeros of the function y=9x^2-12x-33.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form

Start with the given equation

Add to both sides

Factor out the leading coefficient

Take half of the x coefficient to get (ie ).

Now square to get (ie )

Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of does not change the equation

Now factor to get

Distribute

Multiply

Now add to both sides to isolate y

Combine like terms

Now the quadratic is in vertex form where , , and . Remember (h,k) is the vertex and "a" is the stretch/compression factor.

Check:

Notice if we graph the original equation we get:

Graph of . Notice how the vertex is (,).

Notice if we graph the final equation we get:

Graph of . Notice how the vertex is also (,).

So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.

RELATED QUESTIONS
John used completing the square to find the zeros of the function y=9x^2-12x-33. (answered by ankor@dixie-net.com)

Bill used completing the square to find the zeroes of the function {{{y=9x^2-12x-33}}}.... (answered by MathLover1,Edwin McCravy)

Use the Completing the Square method to find the vertex form of the quadratic function... (answered by Mathtut,nerdybill)

Use the Completing the Square method to find the vertex form of the quadratic function... (answered by jim_thompson5910)

Find the zeros of the function, state the multitplicity of multiple zeros:... (answered by ewatrrr)

Find a rational zero of the polynomial function and use it to find all the zeros of the... (answered by stanbon)

Find a rational zero of the polynomial function and use it to find all the zeros of the... (answered by Fombitz)

Find a rational zero of the polynomial function and use it to find all the zeros of the... (answered by stanbon)

Use the method of completing the square to find the standard form of the quadratic... (answered by MathLover1)