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8090 [49]
3 years ago
9

Find the vertex of y=5-4x-x^2

Mathematics
2 answers:
SSSSS [86.1K]3 years ago
3 0
The answer is (h,k)
(-2,9)
Levart [38]3 years ago
3 0

Answer:

(-2,9)

Step-by-step explanation:

rewrite in vertex form: y= -(x+2)^2+9

(-2,9)

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First, draw a diagram to visualize the situation:

As we can see, the difference between the x-coordinates of the points is the length of one leg of a right triangle, and the difference between the y-coordinates is the length of the other leg.

Then, for the given points (-5,4) and (8,-3), the distance given by the Pythagorean Theorem is:

\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\  \\ =\sqrt{(8--5)^2+(-3-4)^2} \\  \\ =\sqrt{(13)^2+(-7)^2} \\  \\ =\sqrt{169+49} \\  \\ =\sqrt{218} \\  \\ \approx14.7648... \end{gathered}

Therefore, the distance between the points (-5,4) and (8,-3) is: √218.

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