Quadratic Functions and Graphs: math test, Grade 9 – download the PDF

1 Features of a parabola / 3 pts

Let \(y = x^2 - 8x + 12\).

1. Give \(a\), \(b\), \(c\) and say whether the parabola opens up or down.
2. Find the axis of symmetry.
3. Find the vertex and the minimum or maximum value.

2 Solving by factoring / 4 pts

Solve each equation by factoring.

1. \(x^2 + 2x - 35 = 0\)
2. \(x^2 - 11x + 24 = 0\)

3 Reading a vertex form / 3 pts

Let \(f(x) = -2(x - 3)^2 + 18\).

1. Give the vertex and the direction of the opening.
2. Find the \(y\)-intercept.
3. Find the zeros of \(f\).

4 Transformations and equations / 4 pts

1. Describe the transformations that turn \(y = x^2\) into \(y = \dfrac{1}{2}(x + 2)^2 - 3\), and give the vertex.
2. A parabola has vertex \((1, 4)\) and passes through \((3, 0)\). Write its equation in vertex form.

5 Reading a graph / 3 pts

The graph below shows a parabola with points \(A\), \(B\), \(V\), and \(C\) marked.

1. Read the coordinates of \(A\), \(B\), \(V\), and \(C\) and name the axis of symmetry.
2. Write the equation of the parabola in the form \(y = a(x - x_A)(x - x_B)\), then in standard form.

6 A stone off a bridge / 3 pts

A stone is thrown upward from a bridge. Its height in feet after \(t\) seconds is \(h(t) = -16t^2 + 16t + 20\). A calculator is allowed.

1. At what time is the stone at its highest point?
2. What is the maximum height?
3. When does the stone reach the ground? Round to the nearest hundredth.