Y=-x^2+20x-64 what is the max height

Mathematics

1 answer:

Inessa [10]3 years ago

8 0

Answer:

Step-by-step explanation:

The maximum height is the y-coordinate of the vertex

given a quadratic in standard form : ax² + bx + c : a ≠ 0

then the x-coordinate of the vertex is

$x_{vertex}$ = - $\frac{b}{2a}$

y = - x² + 20x - 64 is in standard form

with a = - 1, b = 20 and c = - 64, hence

$x_{vertex}$ = - $\frac{20}{-2}$ = 10

substitute x = 10 into the equation for y

y = - (10)² + 20(10) - 64 = 36 ← max height

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Graphs of 3 functions are shown below. In two or more sentences, explain whether or not the inverse of each graph is a function.

S_A_V [24]

The first and third graphs inverse will still be functions (although the first is iffy as it is hard to tell if when any x values are equal, if there are equal x values it will not be a function because then there will be multiple y values for a single x value. In simpler terms, if there is a truly horizontal line in that first graph, its inverse will not be a function as it will fail the vertical line test.)

The second graph will not be a function as each x value will have two y values, so it fails "the vertical line test".

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3 years ago

Please help me with this for 20 points

astra-53 [7]

Answer:

$\large a)\ f(x)=\dfrac{5}{9}(x-32)\\\\b)\ f^{-1}(x)=\dfrac{9}{5}x+32\\\\9^oC=48.2^oF$

Step-by-step explanation:

$C=\dfrac{5}{9}(F-32)\\\\a)\ f(x)=\dfrac{5}{9}(x-32)\\\\b)\ C=\dfrac{5}{9}(F-32)\\\\\text{solve for F}\\\\\dfrac{5}{9}(F-32)=C\qquad\text{multiply both sides by 9}\\\\5(F-32)=9C\qquad\text{divide both sides by 5}\\\\F-32=\dfrac{9}{5}C\qquad\text{add 32 to both sides}\\\\F=\dfrac{9}{5}C+32\\\\f^{-1}(x)=\dfrac{9}{5}x+32$