The height of a projectile fired vertically into the air (neglecting air resistance) at an initial velocity of 96 feet per second is a function of the time and is given by the equation f (x) = 96x - 16x2, where x represents the time. Find the highest point reached by the projectile.

Q: What point on the function, y = 3x2 is the closest to (0, 1)?

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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A:

Q: Determine whether the equation defines y as a function of x : 4x = y2

A: For x=1,

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A: We will solve the equation for y first.

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A: The given equation is 2x=y4-16.

Q: The y-intercept of the function is

A:

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A: Solution is in step 2

Q: In the piecewise function in the picture, what does y equal when x=3?

A:

Q: Use the graph of f(x) = x3 to write an equation for the function

A: the graph f(x) reflected over the y-axis and then moved 2 units left and 2 units down.  So new…

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A: A quarter falls of a building that is 144 feet tall.The equation for height as a function of time is…

Q: Find the points of intersection of the graphs of the functions y = x2 + 1 and y = 4x

A: Given functions:                     y = x2+1   ... (1)                     y = 4x      ... (2)

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A:

Q: Enter the equation of the function, g(x), whose graph is the result of f(x) = √√x shifted right 6…

A: Please see the below picture for detailed solution.

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A: The difference quotient is calculated by . First, evaluate the value of f(x+h).

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A:

Q: hat is the slope of the function f(x) =6x3 -7x +4 when x=1?

A: The function is given as f(x) =6x3 -7x +4

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A:

Q: In the given equation , sketch the graph of the function   y = 3- lxl

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A: Use the given value and logarithms to find the value of x

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A: Slope of graph of function at given point is first derivative of function at that point.

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Q: Sketch the curve. Show your solutions. f(x) = x4 - 6x2

A: Consider the given: fx=x4−6x2Apply exponent rule:     ab+c=abacfx=x2x2−6x2Factor out common term…

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Q: find horizontal and vertical intercept of f(x)= -2|x+1|+6 and graphing the function

A: The given function:

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A: Use formula

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A: Let's find.

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Q: Enter an equation for the line of Symbrietry for the function f(x)=4x2+16X=9

A:

Q: Find an equation of the line tangent to the graph of f(x) = - 3-6x at (-5,- 153).

A: Given : fx = -3-6x2

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Q: Find the point at which the line f(x)3 4x6 intersects the line g(x) =-4 +2

A: