Question 252702
Let's start with the first equation and then repeat process for second:
(i) {{{ y = x^2 + 6x - 10}}}
STEP #1: re write the equation as
(ii) {{{X^2 + 6X + ___ = 10 + ___ }}}
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STEP #2: take 1/2 middle term number and square it. put that answer in the blanks. We get
(iii) {{{X^2 + 6X + 3^2 = 10 + 3^2}}}
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STEP #3: write the left side as a quantity squared and equalling the right.
(iv) {{{(X + 3)^2 = 19}}}
This is vertex form.
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(v)  y = x^2 - 9x + 3
STEP #1: re write the equation as
(ii) {{{X^2 - 9X + ___ = 3 + ___ }}}
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STEP #2: take 1/2 middle term number and square it. put that answer in the blanks. Sometimes it's easier to say [middle number/2]. Don't forget your signs. We get
(iii) {{{X^2 - 9X + (-9/2)^2 = 3 + (-9/2)^2}}}
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STEP #3: write the left side as a quantity squared and equalling the right.
(iv) {{{(X - 9/2)^2 = (93/4)}}}
This is vertex form.