Find the vertex of the following equation: y = -0.25x2 + -1.5x + 6

Hi there!

Solve for the vertex by completing the square:

y = -0.25x² - 1.5x + 6

Factor out a negative:

y = -(0.25x² + 1.5x) + 6

Remember that a square binomial is:

a² + 2ab + b²

We know that:

a² = 0.25, so a = 0.5

1.5 = 2ab, so:

1.5 = 2(0.5)b

b = 1.5

b² = 2.25

Thus:

y = -(0.25x² + 1.5x + 2.25) + 6 - (-2.25)

Simplify:

y = -(0.5x + 1.5)² + 8.25

Find the vertex by factoring out 0.5:

y = -0.5(x + 3)² + 8.25

Thus, the vertex is:

(-3, 8.25)