Interactive practice questions
A frisbee is thrown upward and away from the top of a mountain that is $120$120 metres tall.
The height, $y$y, of the frisbee at time $x$x in seconds is given by the equation $y=-10x^2+40x+120$y=−10x2+40x+120.
This equation is graphed below.
A Cartesian plane has the $x$x-axis ranging from $0$0 to $6$6 and the $y$y-axis ranging from $0$0 to $200$200. The $x$x-axis is marked at major intervals of $2$2 units and minor intervals of $1$1 unit. The $y$y-axis is marked at major intervals of $50$50 units and minor intervals of $10$10 units. A parabola that opens downward is plotted on the Cartesian plane. The curve begins at point $\left(0,120\right)$(0,120) and rises to the right towards the vertex at point $\left(2,160\right)$(2,160). From point $\left(2,160\right)$(2,160), the curve descends towards the point $\left(6,0\right)$(6,0). The points and their coordinates are not explicitly given nor labeled.
What is the $y$y-value of the $y$y-intercept of this graph?
Which of the following descriptions corresponds to the value of the $x$x-intercept?
The maximum height reached by the frisbee.
The amount of time it takes for the frisbee to reach the ground.
The height of the mountain.
The amount of time it takes for the frisbee to reach its maximum height.
Given that the $x$x-value of the vertex is $2$2, what is the maximum height reached by the frisbee?
A rectangle is to be constructed with $80$80 metres of wire. The rectangle will have an area of $A=40x-x^2$A=40x−x2, where $x$x is the length of one side of the rectangle.
The formula for the surface area of a sphere is $S=4\pi r^2$S=4πr2, where $r$r is the radius in centimetres.
A compass is accidentally thrown upward and out of an air balloon at a height of $100$100 feet. The height, $y$y, of the compass at time $x$x in seconds is given by the equation
$y=-20x^2+80x+100$y=−20x2+80x+100