Question

extra practice1. convert $y = x^2 + 4x - 12$ to factored form.2. convert $y = (x + 7)(x - 1)$ to standard form.3. convert $y = (x - 9)^2 + 13$ to standard form.4. convert $y = x^2 + 6x + 8$ to vertex form.1. which equation is equivalent to $y = -2x^2 + 32x - 126$?a $y = -2(x + 8)^2 + 2$b $y = -2(x - 7)(x - 9)$c $y = -2(x + 7)(x + 9)$d $y = (-2x - 7)(x - 18)$eoc style questionconsider the graph of the following quadratic equation.$y = -x^2 - 10x + 24$what is the $y$-value of the vertex?$y = \square$

Explanation:

Step1: Factor quadratic (Problem 1)

Find two numbers: $6$ and $-2$ (sum $4$, product $-12$).
$y = x^2 + 4x - 12 = (x+6)(x-2)$

Step2: Expand factored form (Problem 2)

Use FOIL method:
$y=(x+7)(x-1)=x^2 -x +7x -7 = x^2 +6x -7$

Step3: Expand vertex form (Problem3)

Expand square, then simplify:
$y=(x-9)^2 +13 = x^2 -18x +81 +13 = x^2 -18x +94$

Step4: Complete the square (Problem4)

Group $x$-terms, add/subtract $9$:
$y=x^2+6x+8=(x^2+6x+9)-9+8=(x+3)^2 -1$

Step5: Factor given quadratic (Multiple Choice)

Factor out $-2$, then factor trinomial:
$y=-2x^2+32x-126=-2(x^2-16x+63)=-2(x-7)(x-9)$

Step6: Find vertex y-value (EOC Question)

Use vertex $x=-\frac{b}{2a}=-\frac{-10}{2(-1)}=-5$. Substitute:
$y=-(-5)^2 -10(-5)+24=-25+50+24=49$

Answer:

1. $y=(x+6)(x-2)$
2. $y=x^2+6x-7$
3. $y=x^2-18x+94$
4. $y=(x+3)^2 -1$

Multiple Choice: B. $y=-2(x-7)(x-9)$
EOC Question: $y=49$