SOLUTION: 1. A ball follows a flight given by y = 20x - x^2 + 6 where x represents the horizontal distance traveled in feet and y represents the height of the ball in feet. What will be the

Question 57244: 1. A ball follows a flight given by y = 20x - x^2 + 6 where x represents the horizontal distance traveled in feet and y represents the height of the ball in feet. What will be the maximum height of this ball if it is thrown?
2. If x=2, x=-3 and x=0 are zeros of a polynomial, what is a possible equation for this polynomial?
3. What is the vertex of the graph given by
y=2x^2 - 4x + 3? Would the graph be a shift of y=2x^2?
4. Write the equation of the parabola given by y=2x^2-4x+3 in "standard" form.
Thank you very much!!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A ball follows a flight given by y = 20x - x^2 + 6 where x represents the horizontal distance traveled in feet and y represents the height of the ball in feet. What will be the maximum height of this ball if it is thrown?
:
Put the equation in the familiar form: y = ax^2+ bx + c
:
y = -x^2 + 20x + 6:
:
The value of x, at maximum height (y), will occur at the vertex. We can use the vertex formula: x = -b/(2a)
:
In your equation: a = -1; b = 20
:
x = -20/(2*-1)
x = -20/-2
x = 10 ft is horizontal distance
:
To find the max height substitute 5 for x in the orginal equation:
y = 20x - x^2 + 6
y = 20(10) - 10^2 + 6
y = 200 - 100 + 6
y = 106 feet is max height
:
:
:
2. If x=2, x=-3 and x=0 are zeros of a polynomial, what is a possible equation for this polynomial?
:
That would give us factors of (x-2)(x+3) and x
:
FOIL the 1st two factors and you have:
x(x^2 + x - 6) = x^3 + x^2 - 6x
:
y = x^3 + x^2 - 6x; would give you zeros of -3, 0, and +2
:
:
:
3. What is the vertex of the graph given by y = 2x^2 - 4x + 3?
:
I gave you the vertex formula above. In this equation a = 2, b = -4, since the coefficient of x^2 is positive, there would be a minimum at the vertex
:
Would the graph be a shift of y = 2x^2? I would say yes
:
:
:
4. Write the equation of the parabola given by y = 2x^2-4x+3 in "standard" form. I think that would be: 2x^2 - 4x + 3 = 0

RELATED QUESTIONS
Please Help Me! 1. The path of a ball thrown into the air from a height of 3 feet is... (answered by ankor@dixie-net.com)

I have collected data has follows for a projectile we threw in class: Estimated launch... (answered by solver91311)

A ball is thrown across a playing field. Its path is given by the equation... (answered by nerdybill)

A ball is thrown across a playing field. Its path is given by the equation y =... (answered by josmiceli)

The height y (in feet) of a ball thrown by a child is y=-\frac{1}{16}x^2 + 6 x + 3... (answered by Alan3354)

The height y (in feet) of a ball thrown by a child is given by the equation y=... (answered by fractalier)

The path that a motorcross dirt bike rider follows during a jump is given by... (answered by Alan3354)

The height h(in feet) of a model rocket in flight is modeled by h(x) = -5/6x2 + 20x,... (answered by josmiceli)

a ball is thrown across a playing field. it’s path is by the equation y=-0.005x^2 +x+5... (answered by Alan3354,ewatrrr)