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Complete the statements below that show y = 8x2 + 32x + 17 being converted to vertex form. Factor out the leading coefficient. y = 8(x2 + 4x) + 17 Form a perfect-square trinomial. y = 8(x2 + 4x + ) + 17 +

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andrewdunn
8(x^2 + 4x +4) + 17 + -32
kudzordzifrancis
ANSWER

[tex]y=8(x^2+4x+4)+17-32[/tex]

EXPLANATION

We were given [tex]y=8x^2+32x+17[/tex].

To convert to vertex form, We factor out the leading coefficient which is 8.

[tex]y=8(x^2+4x)+17[/tex]

Next, we form a perfect square by adding and subtracting [tex]8(2)^2[/tex] to get;

[tex]y=8(x^2+4x)+8(4)+17-8(4)[/tex]

We factor and combine the first two terms with a common factor of 8 to get,

[tex]y=8(x^2+4x+4)+17-8(4)^2[/tex]

This simplifies to

[tex]y=8(x^2+4x+4)+17-32[/tex]

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