Algebra 1 Graphing Quadratic Functions and Transformations Test with Point Values (PDF)

Identify the vertex, the axis of symmetry, and the direction of opening of \(y = 2(x – 3)^{2} – 1\).

Find the vertex of \(y = x^{2} – 10x + 16\).

Find the y-intercept and the x-intercepts of \(y = x^{2} – x – 6\).

Graph \(y = x^{2} – 2x – 3\) and label the vertex.

Describe how the graph of \(y = -(x + 3)^{2} + 2\) is obtained from \(y = x^{2}\).

Write \(y = x^{2} + 4x + 1\) in vertex form.

A ball’s height in feet is \(h = -16t^{2} + 32t + 6\) after \(t\) seconds.

1. Find the time of the maximum height. (1 point)
2. Find the maximum height. (1 point)
3. Find the height at \(t = 0\). (1 point)

A rectangular pen is built with 60 feet of fence. One side is \(x\) feet and the other is \(30 – x\) feet.

1. Write the area \(A\) as a function of \(x\). (1 point)
2. Find the value of \(x\) that gives the greatest area. (1 point)
3. Find the greatest area. (1 point)

Which function has the greater minimum value: \(f(x) = (x + 1)^{2} + 5\) or \(g(x) = x^{2} – 6x + 12\)? Show your work.