Answer:
y =- (x + [tex]\frac{3}{2}[/tex])² + [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square
• the coefficient of the x² term must be 1
Take out a factor of - 1 from - x² - 3x
y = -(x² + 3x) - 1
• add/subtract (half the coefficient of the x-term)² to x² + 3x
y = - (x² + 2([tex]\frac{3}{2}[/tex])x + [tex]\frac{9}{4}[/tex] - [tex]\frac{9}{4}[/tex]) - 1
y = -(x + [tex]\frac{3}{2}[/tex])² + [tex]\frac{9}{4}[/tex] - [tex]\frac{4}{4}[/tex]
y = - (x + [tex]\frac{3}{2}[/tex])² + [tex]\frac{5}{4}[/tex] ← in vertex form
