Solving Quadratic Equations: Algebra 1 Math Test – PDF Download

Question 1: Square roots (2 points)

Solve each equation.

1. \(3x^{2}=48\) (1 point)
2. \((x+1)^{2}=25\) (1 point)

Question 2: Factoring (2 points)

Solve each equation.

1. \(x^{2}+3x-40=0\) (1 point)
2. \(3x^{2}-x-2=0\) (1 point)

Question 3: Complete the square (3 points)

Solve \(x^{2}+6x-2=0\) by completing the square. Give exact solutions, then round to the nearest hundredth.

Question 4: Quadratic formula (3 points)

Solve \(2x^{2}-3x-4=0\) using the quadratic formula. Give exact solutions, then round to the nearest hundredth.

Question 5: Discriminant (2 points)

Answer each part.

1. Find the discriminant of \(3x^{2}-6x+4=0\) and state how many real solutions it has. (1 point)
2. Find the value of \(k\) for which \(x^{2}-8x+k=0\) has exactly one real solution. (1 point)

Question 6: Use a graph (3 points)

The graph of \(y=x^{2}-4x-5\) is shown.

1. Use the graph to solve \(x^{2}-4x-5=0\). (1 point)
2. Name the vertex and the axis of symmetry. (1 point)
3. For which values of \(x\) is \(y < 0\)? (1 point)

Question 7: Rectangle (2 points)

A rectangular banner is 5 feet longer than it is wide, and its area is 84 square feet. Find its width and length.

Question 8: Ball flight (2 points)

A ball is hit upward and its height in feet after \(t\) seconds is \(h(t)=-16t^{2}+40t+24\). The graph is shown.

1. After how many seconds does the ball hit the ground? (1 point)
2. Explain why one solution of the equation is not used. (1 point)

Question 9: No real solution (1 point)

A student says that \(x^{2}=-9\) has the solutions \(x=3\) and \(x=-3\). Explain the error.

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