Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Modelling Relationships: Linear and Quadratic Functions, Exercise 41: Exercise 3O

Use the information shown in the graph to find an expression for the quadratic function. Write your final answer in the form $f\left(x\right)=a{x}^2+bx+c$.

The graph of quadratic function $y=f\left(x\right)$ has $x$-intercepts $(-1,0)$ and $\left(3,0\right)$. The function has a maximum value of $4$.

Find the equation of the axis of symmetry for the graph of $y=f\left(x\right)$.

The graph of quadratic function $y=f\left(x\right)$ has $x$-intercepts $(-1,0)$ and $\left(3,0\right)$. The function has a maximum value of $4$.

Write down the coordinates of the vertex for the graph of $y=f\left(x\right)$.

The graph of quadratic function $y=f\left(x\right)$ has $x$-intercepts $(-1,0)$ and $\left(3,0\right)$. The function has a maximum value of $4$.

Find an equation for $f$ in the form of $f\left(x\right)=a(x-h{)}^2+k$, where $a,h,k$ are constants to be determined.

The graph of quadratic function $y=f\left(x\right)$ has $x$-intercepts $(-1,0)$ and $\left(3,0\right)$. The function has a maximum value of $4$.

A translation of the graph of $y=f\left(x\right)$ right $4$ units and down $5$ units results in graph of $y=g\left(x\right)$. find an expression for the function $g\left(x\right)$ in the form of $f\left(x\right)=a{x}^2+bx+c$.

The table and graph are representations of the predicted height, $h$ metres, of a model rocket, $t$ seconds after it is launched.

Write down the coordinates of the vertex of the graph and then explain its meaning in terms of the context of the graph.

The table and graph are representations of the predicted height, $h$ metres, of a model rocket, $t$ seconds after it is launched.

Find an equation for $h\left(t\right)$ and give the domain.

The table and graph are representations of the predicted height, $h$ metres, of a model rocket, $t$ seconds after it is launched.

If the predicted height of the model rocket $2.4$ seconds after launch is $b$ metres. find the value of $b$.