Quadratic Functions and Equations: math test, Grade 11 – download the PDF

1 Vertex form / 3 pts

Let \(f(x) = x^2 - 8x + 11\).

1. Write \(f(x)\) in vertex form by completing the square.
2. Give the vertex, the axis of symmetry and the y-intercept.

2 Factoring / 4 pts

1. Factor \(2x^2 - 7x - 15\).
2. Factor \(4x^2 - 81\).
3. Solve \(2x^2 - 7x - 15 = 0\).

3 Quadratic formula (calculator allowed) / 4 pts

Solve \(2x^2 + 3x - 7 = 0\). Give the exact solutions, then round to the nearest hundredth.

4 The discriminant / 3 pts

1. How many real solutions does \(x^2 - 6x + 9 = 0\) have?
2. Are the solutions of \(3x^2 - 2x + 4 = 0\) real or complex?
3. Find \(k\) so that \(2x^2 - 5x + k = 0\) has exactly one real solution.

5 Inequalities / 3 pts

Solve each inequality.

1. \(x^2 - 2x - 8 \leq 0\)
2. \(x^2 + 3x > 10\)

6 A water jet (calculator allowed) / 3 pts

The water from a fountain follows the curve \(h(x) = -0.25x^2 + 2x + 1.75\), where \(x\) is the horizontal distance in feet and \(h\) the height in feet.

1. Find the maximum height of the jet.
2. At what horizontal distances is the water \(4.75\) feet high?
3. How far from the nozzle does the water land? Round to the nearest tenth of a foot.