# Applications of quadratics using graphs

## Interactive practice questions

A frisbee is thrown upward and 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

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

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=40xx2, where $x$x is the length of one side of the rectangle.

On Mercury the equation $d=1.5t^2$d=1.5t2 can be used to approximate the distance in metres, $d$d, that an object falls in $t$t seconds, if air resistance is ignored.

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.

### Outcomes

#### 10D.QR4.02

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