Algebra 2 Quadratics Complex Solutions Test

Contents

This algebra 2 quadratics complex solutions test checks quadratic equations with complex solutions in 45 minutes, with 8 questions for a total of 20 points.

This test has 8 questions worth 20 points in all. Allow 45 minutes. Show every step, write complex solutions in the form a + bi, and simplify radicals. A calculator is not needed. Partial credit is given for correct work.

Test information

Grade: Algebra 2
Chapter: Quadratic Equations with Complex Solutions
Common Core: N-CN.C.7, A-REI.B.4b
Time: 45 minutes
Total: 20 points (Question 1: 2 pts; Question 2: 2 pts; Question 3: 2 pts; Question 4: 3 pts; Question 5: 3 pts; Question 6: 2 pts; Question 7: 3 pts; Question 8: 3 pts)

Algebra 2 Quadratics Complex Solutions Test: questions 1–5

Question 1: Discriminant and solutions (2 points)

For each equation, find the discriminant and state the number and type of solutions.

\(x^{2}-4x+7=0\) (1 point)
\(2x^{2}+5x-3=0\) (1 point)

Question 2: Read a graph (2 points)

The graph of \(y=x^{2}-4x+6\) is shown.

The graph of y = x² − 4x + 6.

How many real solutions does \(x^{2}-4x+6=0\) have? (1 point)
Find the discriminant and describe the solutions. (1 point)

Question 3: Square root method (2 points)

Solve each equation.

\(4x^{2}+100=0\) (1 point)
\((x+3)^{2}=-16\) (1 point)

Question 4: Quadratic formula (3 points)

Solve \(x^{2}-6x+25=0\).

Question 5: Complete the square (3 points)

Solve \(x^{2}+10x+34=0\) by completing the square.

Algebra 2 Quadratics Complex Solutions Test: questions 6–8

Question 6: A quadratic with fractions (2 points)

Solve \(x^{2}+x+1=0\). (2 points)

Question 7: Solutions in the plane (3 points)

The points \(p\) and \(q\) are the two solutions of \(x^{2}+bx+c=0\), where \(b\) and \(c\) are real.

The two solutions of x² + bx + c = 0 plotted in the complex plane.

Write \(p\) and \(q\) as complex numbers. (1 point)
Find \(b\). (1 point)
Find \(c\). (1 point)

Question 8: Will the balloon reach 20 feet? (3 points)

Sofia launches a water balloon. Its height in feet after \(t\) seconds is \(h=-16t^{2}+32t\). Does the balloon ever reach a height of 20 ft? Solve an equation and explain.