Algebra 2 Forms of Quadratic Functions Test with Point Values (PDF)

Algebra 2 math test: Forms of Quadratic Functions – Maths PDF

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This quadratic forms test for Algebra 2 covers forms of quadratic functions (Common Core A-SSE.B.3a, A-SSE.B.3b, F-IF.C.8a), with a free PDF to print.

This 45-minute test on the forms of quadratic functions has 9 questions worth 20 points in total. The questions move from direct skills to multi-step problems. Show your work, because partial credit is given for a correct setup and sound reasoning.

Time and points

About this test

Grade: Algebra 2
Chapter: Forms of Quadratic Functions
Standards: A-SSE.B.3a, A-SSE.B.3b, F-IF.C.8a
Time: 45 minutes
Total: 20 points

Quadratic forms test: questions

Question 1 – Zeros from factored form [2 pts]

Find the zeros and the axis of symmetry of \(f(x) = (x + 6)(x – 2)\).

Question 2 – Complete the square [3 pts]

Write \(f(x) = x^{2} + 6x + 1\) in vertex form and give the vertex.

Question 3 – Vertex from standard form [2 pts]

Find the vertex of \(g(x) = 3x^{2} – 12x + 7\) and state whether it is a maximum or minimum.

Question 4 – Equation from a graph [2 pts]

Vertex (2, 4); the curve passes through (0, 0).

The parabola has vertex \((2, 4)\) and passes through the origin. Write its equation in vertex form.

Question 5 – Projectile [2 pts]

Rocket height h(t).

A rocket’s height is \(h(t) = -16t^{2} + 96t\) feet. Find the maximum height and the time it occurs.

Question 6 – Revenue [2 pts]

R(p) = -2p(p – 30).

The revenue from a school fundraiser is \(R(p) = -2p^{2} + 60p\) dollars at price \(p\). Write \(R\) in factored form and find the price that gives the maximum revenue.

Question 7 – Choose the form [2 pts]

For \(f(x) = x^{2} – 6x + 8\), find (a) the zeros by factoring and (b) the vertex.

Question 8 – Complete the square, a = 2 [3 pts]

Write \(f(x) = 2x^{2} – 8x + 3\) in vertex form.

Question 9 – Find the error [2 pts]

Noah wrote that the vertex of \(f(x) = (x + 3)^{2} – 1\) is \((3, -1)\). Explain his error and give the correct vertex.

Key facts behind this quadratic forms test

Key facts

Standard form ax² + bx + c: y-intercept c.
Factored form a(x – r)(x – s): zeros r and s.
Vertex form a(x – h)² + k: vertex (h, k) and extreme value k.
Complete the square: add and subtract (b/2a)².
a > 0 opens up (minimum); a < 0 opens down (maximum).

How to use this quadratic forms test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Algebra 2 chapters: Algebra 2 math.

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