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G( x )= a(x^2)+bx+cConvert it to vertex form (also known as standard form) by putting the values for a,h and k into the correct boxes.G(x)=a(x-h)^2+kIdentify the vertex(x,y)General form: G( x )=-7 x^2+-9 x +-4 Vertex form: G( x )= Answer for part 1 and coordinate 1 (x- Answer for part 1 and coordinate 2 )^2 +Answer for part 1 and coordinate 3Vertex: (Answer for part 2 and coordinate 1,Answer for part 2 and coordinate 2)

G X Ax2bxcConvert It To Vertex Form Also Known As Standard Form By Putting The Values For Ah And K Into The Correct BoxesGxaxh2kIdentify The VertexxyGeneral For class=

Answer :

The vertex form of G(x) is

[tex]G(x)=-7(x-\frac{9}{2})^2-\frac{583}{4}[/tex]

[tex]\text{Vertex}=(\frac{9}{2},-\frac{583}{4})[/tex]

STEP - BY - STEP EXPLANATION

What to find?

Vertex form of the given equation.

Given:

G(x) = - 7x² + -9x + -4

We can re-write the above as:

G(x) = -7x² - 9x - 4

To write the above in a vertes form, we wil follow the steps below:

Step 1

Insert a parenthesis before x² and after 9x.

G(x) = -7(x²-9x) - 4

Step 2

Add/subtract the square half of the co-efficient of x.

That is; half square of -9 = (-9/2)² = 81/4

So that we have:

G(x) = -7(x² - 9x + 81/4) -7(81/4) - 4

Step 3

Simplify

[tex]\begin{gathered} G(x)=-7(x^2-9x+\frac{81}{4})-7(\frac{81}{4})-4 \\ \\ =-7(x^2-9x+\frac{81}{4})-\frac{567}{4}-4 \\ \\ =-7(x^2-9x+\frac{81}{4})-\frac{567-16}{4} \\ \\ =-7(x^2-9x+\frac{81}{4})-\frac{583}{4} \end{gathered}[/tex]

Step 4

Factorize the expression in the parenthesis.

[tex]G(x)=-7(x-\frac{9}{2})^2-\frac{583}{4}[/tex]

Hence, the vertex form is G(x) = -7(x- 9/2)² + -583/4

The vertex

Given the general formula y=a(x-h)² + + k

The vertex is (h, k).

Comparring the general form to our answer in step 4. Observe that h=9/2 and k=-583/4

Therefore, the vertex is ( 9/2 , -583/4)

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