Question 252708
Let's start with the first equation and then repeat process for second:
(i) {{{y = 3x^2 + 18x + 30}}}
STEP #1: factor out the 3 from the first two terms to get
(ii) {{{3(x^2 + 6X + ___ ) + 30 - ____}}}
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STEP #2: take 1/2 middle term number and square it. Multiply it by 3 and put that answer in the blanks. We get
(iii) {{{3(x^2 + 6X + 3^2) + 30 - 3*3^2}}}
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STEP #3: write the left side as a quantity squared and equalling the right.
(iv) {{{y = 3(X+3)^2 + 3}}}
This is vertex form.
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(v) y= -2x^2+28x-7
STEP #1: factor out -2 from the first two terms to get
(ii) {{{-2(x^2 - 14x + ___ ) - 7 - ____}}}
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STEP #2: take 1/2 middle term number and square it. Multiply it by -2 and put that answer in the blanks. Sometimes it's easier to say [middle number/2]. Don't forget your signs. We get
(iii) {{{-2(x^2 - 14x + (-7)^2) - 7 - (-98)}}} 
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STEP #3: write the left side as a quantity squared and equalling the right.
(iv) {{{-2(x - 7)^2 + 91}}}
This is vertex form.