Question

What is the turning point of the parabola with the equation?
y=27(x-64)squared+43
A: (-64,-43) B: (64,43) C: (64,-43) D: (1728,43) E: (-64,43)

Answer 1

The turning point of the parabola is (64, -43)

What is a turning point?

Turning point is that point on a parabolic curve in which the gradient of the curve changes value.

It is also the point on the curve in which the curve starts rising or falling.

Analysis:

$27(x-64)^{2}$ + 43

27(x-64)(x-64) + 43

27($x^{2}$ -64x -64x +4096) + 43

27$x^{2}$ -3456x +110592 +43

27$x^{2}$ -3456x +110635

at turning point dy/dx = 0

dy/dx = 54x - 3456

54x - 3456 = 0

54x = 3456

x = 3456/54 = 64

To find the value of y at x = 64

27$(64)^{2}$ -3456(64) +110635

110592 - 221184 +110635 = -43

Therefore the turning point of the parabola is (64, -43)

Learn more about Turning point: brainly.com/question/11123173

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