Modelling a Ball Thrown in the Air
Click to play and pause the trajectory of the ball.
$t$ is the time and $h$ is the height above the ground.
What is the maximum height of the ball?
What is the time when the ball is at the maximum height?
What is the time when the ball lands on the ground?
We can create a model of the height of the ball in terms of time. The equation is $h\left(t\right)=-2t^2+8t$ for $0 \le t \le 4$.
Click to see how the model is graphed. For this graph, the x-axis represents
A function that has the form $f\left(x\right)=ax^2+bx+c$ where $a\ne 0$ is called a $\fbox{q _ _ _ _ _ _ _ _ }$ function.
The shape of the graph of a quadratic function is a $\fbox{p _ _ _ _ _ _ _ }$.
The maximum point or minimum point on the graph of a quadratic function is called the $\fbox{v _ _ _ _ _ }$.
In this example, the coordinates of the vertex are
The vertical line that goes through the vertex is called the axis of $\fbox{s _ _ _ _ _ _ _ }$.
In this example, the axis of symmetry has the equation
Example
Graph the function $f\left(x\right)=\frac{1}{4}x^2+x-3$ on the grid above.
Write down the coordinates of the $x$-intercepts. Separate your answers with a comma.
Write down the coordinates of the $y$-intercept.
Write down the coordinates of the vertex.
Write down the equation of the axis of symmetry.
State the domain of this function.
State the range of this function.