Question

Please help! I've tried this problem many times but continue to get it wrong.

Answer 1

Answer:

y =- (x + $\frac{3}{2}$)² + $\frac{5}{4}$

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($\frac{3}{2}$)x + $\frac{9}{4}$ - $\frac{9}{4}$) - 1

y = -(x + $\frac{3}{2}$)² + $\frac{9}{4}$ - $\frac{4}{4}$

y = - (x + $\frac{3}{2}$)² + $\frac{5}{4}$ ← in vertex form