The vertex form of y = x² + 16x - 71 is (x + 8)² - 135
Step-by-step explanation:
The vertex form of the quadratic function y = ax² + bx + c, is
y = a(x - h)² + k, where
∵ The quadratic function is y = x² + 16x - 17
- Compare it with the general form of the quadratic function above
∴ a = 1 , b = 16 and c = -71
∵ [tex]h=\frac{-b}{a}[/tex]
- Substitute the value of a and b is h
∴ [tex]h=\frac{-16}{2(1)}[/tex]
∴ [tex]h=\frac{-16}{2}=-8[/tex]
∵ k = y when x = h
- Substitute x by -8 in the function above
∴ k = (-8)² + 16(-8) - 71
∴ k = 64 - 128 - 71
∴ k = -135
∴ The vertex point is (-8 , -135)
∵ The vertex form is y = a(x - h)² + k
∵ a = 1 , h = -8 , k = -135
- Substitute these values in the vertex form above
∴ y = 1(x - (-8))² + (-135)
∴ y = (x + 8)² - 135
The vertex form of y = x² + 16x - 71 is (x + 8)² - 135
Learn more:
You can learn more about quadratic function in brainly.com/question/9390381
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