which equation represents a graph with a vertex at (1, -6)?\n○ y = 3x² + 6x - 3\n○ y = 3x² - 6x - 3\n○ y =…
which equation represents a graph with a vertex at (1, -6)?\n○ y = 3x² + 6x - 3\n○ y = 3x² - 6x - 3\n○ y = 3x² - 8x - 1\n○ y = 3x² - 3x - 6
Answer
Explanation:
Step1: Recall the vertex formula
For a quadratic function (y = ax^{2}+bx + c), the (x) - coordinate of the vertex is (x=-\frac{b}{2a}).
Step2: Check each option
- Option 1: (y = 3x^{2}+6x - 3) Here (a = 3), (b = 6). Then (x=-\frac{6}{2\times3}=- 1\neq1).
- Option 2: (y = 3x^{2}-6x - 3) Here (a = 3), (b=-6). Then (x =-\frac{-6}{2\times3}=1). Substitute (x = 1) into (y = 3x^{2}-6x - 3), (y=3\times1^{2}-6\times1 - 3=3 - 6 - 3=-6).
- Option 3: (y = 3x^{2}-8x - 1) Here (a = 3), (b=-8). Then (x=-\frac{-8}{2\times3}=\frac{4}{3}\neq1).
- Option 4: (y = 3x^{2}-3x - 6) Here (a = 3), (b=-3). Then (x=-\frac{-3}{2\times3}=\frac{1}{2}\neq1).
Answer:
(y = 3x^{2}-6x - 3) (the second option)