Answer: y = -3(x + [tex]\frac{5}{6}[/tex])² + [tex]\frac{37}{12}[/tex], [tex](-\frac{5}{6}[/tex], [tex]\frac{37}{12})[/tex]
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 + [tex]\frac{5}{3}x[/tex]
y - 1 + -3([tex]\frac{25}{36}[/tex]) = -3(x² + [tex]\frac{5}{3}x[/tex] + [tex]\frac{25}{36}[/tex])
↑ ↓ ↑
[tex]\frac{5}{3*2}[/tex] = [tex](\frac{5}{3*2})^{2}[/tex]
y - 1 - [tex]\frac{25}{12}[/tex] = -3(x + [tex]\frac{5}{6}[/tex])²
y - [tex]\frac{12}{12}[/tex] - [tex]\frac{25}{12}[/tex] = -3(x + [tex]\frac{5}{6}[/tex])²
y - [tex]\frac{37}{12}[/tex] = -3(x + [tex]\frac{5}{6}[/tex])²
y = -3(x + [tex]\frac{5}{6}[/tex])² + [tex]\frac{37}{12}[/tex]
Now, it is in the form of y = a(x - h)² + k where (h, k) is the vertex
Vertex = [tex](-\frac{5}{6}[/tex], [tex]\frac{37}{12})[/tex]
