2 years ago

F(3)= 5x^2 - 4x + 9 evaluate this quadratic function

Mathematics

1 answer:

Neporo4naja [7]2 years ago

6 0

Answer:

$f(3) = 38$

Step-by-step explanation:

Given the quadratic function

$f\left(x\right)=\:5x^2\:-\:4x\:+\:9$

Evaluating the quadratic function

$f\left(x\right)=\:5x^2\:-\:4x\:+\:9$

substitute x = 3

$f\left(3\right)=\:5\left(3\right)^2\:-\:4\left(4\right)\:+\:9$

$f(3) = 45-16+9$

$f(3) = 38$

Therefore,

$f(3) = 38$

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Find the distance between the following points using the Pythagorean theorem: (-5, 4) and (8, -3)

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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.