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ololo11 [35]
3 years ago
9

What equation represents y=2x^2+24x+85 in vertex form

Mathematics
1 answer:
Andrej [43]3 years ago
8 0
Y=a(x-h)^2+k

vertex form is basically completing the square

what you do is
for
y=ax^2+bx+c
1. isolate x terms
y=(ax^2+bx)+c
undistribute a
y=a(x^2+(b/a)x)+c
complete the square by take 1/2 of b/a and squaring it then adding negative and postive inside
y=a(x^2+(b/a)x+(b^2)/(4a^2)-(b^2)/(4a^2))+c
complete square
too messy \
anyway

y=2x^2+24x+85
isolate
y=(2x^2+24x)+85
undistribute
y=2(x^2+12x)+85
1/2 of 12 is 6, 6^2=36
add neagtive and postivie isnde
y=2(x^2+12x+36-36)+85
complete perfect square
y=2((x+6)^2-36)+85
distribute
y=2(x+6)^2-72+85
y=2(x+6)^2+13

vertex form is
y=2(x+6)^2+13
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Step-by-step explanation:

<u>Step 1:</u>

(a + x) (ax + b)

<u>Step 2: Proof</u>

Checking polynomial identity.

(ax+b )(x+a) = FOIL

(ax+b)(x+a)

ax^2+a^2x is the First Term in the FOIL

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(ax+b)(x+a)+bx+ab is the Second Term in the FOIL

Add both expressions together from First and Second Term  

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<u>Step 3: Proof </u>

(ax+b)(x+a) = ax^2 + a^2x + bx + ab

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Trying with numbers now

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