Quadratic Equations with Complex Solutions: Algebra 2 Math Test – PDF Download

Question 1: Discriminant and solutions (2 points)

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

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

Question 2: Read a graph (2 points)

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

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

Question 3: Square root method (2 points)

Solve each equation.

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

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.

1. Write \(p\) and \(q\) as complex numbers. (1 point)
2. Find \(b\). (1 point)
3. 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.

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