Quadratic Relations

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`=−10`x`2+40`x`+120.

This equation is graphed below.

Loading Graph...

a

What is the $y$`y`-value of the $y$`y`-intercept of this graph?

b

Which of the following descriptions corresponds to the value of the $x$`x`-intercept?

The maximum height reached by the frisbee.

A

The amount of time it takes for the frisbee to reach the ground.

B

The height of the mountain.

C

The amount of time it takes for the frisbee to reach its maximum height.

D

c

Given that the $x$`x`-value of the vertex is $2$2, what is the maximum height reached by the frisbee?

Easy

Approx 2 minutes

A rectangle is to be constructed with $80$80 metres of wire. The rectangle will have an area of $A=40x-x^2$`A`=40`x`−`x`2, 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`=4π`r`2, 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`=−20`x`2+80`x`+100

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Solve problems arising from a realistic situation represented by a graph or an equation of a quadratic relation, with and without the use of technology