5.1E: Quadratic Functions (Exercises)

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For the following exercises, write the quadratic function in standard form. Then give the vertex and axes intercepts. Finally, graph the function.

1. \(f(x)=x^{2}-4 x-5\)

2. \(f(x)=-2 x^{2}-4 x\)

For the following exercises, find the equation of the quadratic function using the given information.

3. The vertex is (-2,3) and a point on the graph is (3,6)

4. The vertex is (-3,6.5) and a point on the graph is (2,6) .

For the following exercises, complete the task.

5. A rectangular plot of land is to be enclosed by fencing. One side is along a river and so needs no fence. If the total fencing available is 600 meters, find the dimensions of the plot to have maximum area.

6. An object projected from the ground at a 45 degree angle with initial velocity of 120 feet per second has height, \(h,\) in terms of horizontal distance traveled, \(x,\) given by \(h(x)=\frac{-32}{(120)^{2}} x^{2}+x\). Find the maximum height the object attains.