Question

which equation represents a graph with a vertex at (1, -6)?
○ y = 3x² + 6x - 3
○ y = 3x² - 6x - 3
○ y = 3x² - 8x - 1
○ y = 3x² - 3x - 6

Explanation:

Step1: Recall vertex x-coordinate formula

For quadratic $y=ax^2+bx+c$, $x=-\frac{b}{2a}$

Step2: Test option 1: $y=3x^2+6x-3$

$x=-\frac{6}{2(3)}=-1$ (not 1, eliminate)

Step3: Test option 2: $y=3x^2-6x-3$

$x=-\frac{-6}{2(3)}=1$

Step4: Verify y-value at x=1

$y=3(1)^2-6(1)-3=3-6-3=-6$ (matches vertex)

Step5: Confirm other options (optional)

Option3: $x=-\frac{-8}{2(3)}=\frac{4}{3}
eq1$; Option4: $x=-\frac{-3}{2(3)}=0.5
eq1$

Answer:

B. $y=3x^2-6x-3$