nananna90
26.07.2021 •
Mathematics
Find the vertex of the following equation: y = -0.25x2 + -1.5x + 6
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Ответ:
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)
Ответ:
The answer that matches the graph is B x < 3