Question

Rewrite the equation in vertex form. then find the vertex of the graph. y=-3x^2-5x+1

Answer 1

Answer: y = -3(x + $\frac{5}{6}$)² + $\frac{37}{12}$, $(-\frac{5}{6}$, $\frac{37}{12})$

Step-by-step explanation:

First, you need to complete the square:

y   = -3x² - 5x + 1

-1                    -1  

y - 1 = -3x² - 5x

y - 1 = -3(x² + $\frac{5}{3}x$

y - 1 + -3($\frac{25}{36}$) = -3(x² + $\frac{5}{3}x$ + $\frac{25}{36}$)

           ↑                     ↓            ↑

                                  $\frac{5}{3*2}$ = $(\frac{5}{3*2})^{2}$

y - 1 - $\frac{25}{12}$ = -3(x + $\frac{5}{6}$)²

y - $\frac{12}{12}$ - $\frac{25}{12}$ = -3(x + $\frac{5}{6}$)²

y  - $\frac{37}{12}$ = -3(x + $\frac{5}{6}$)²

y = -3(x + $\frac{5}{6}$)² + $\frac{37}{12}$

Now, it is in the form of y = a(x - h)² + k   where (h, k) is the vertex

Vertex = $(-\frac{5}{6}$, $\frac{37}{12})$