Solving Quadratic Equations: math test, Grade 9 – download the PDF

1 Square root method / 3 pts

Solve.

1. \(2x^2-50=0\)
2. \((x+2)^2=20\) (exact answers, then nearest hundredth)

2 Completing the square / 4 pts

Solve by completing the square.

1. \(x^2-12x+20=0\)
2. \(3x^2+6x-1=0\)

3 Quadratic formula and discriminant / 4 pts

Calculators are allowed.

1. Solve \(2x^2-7x+3=0\) with the quadratic formula.
2. How many real solutions does \(x^2-8x+17=0\) have? Justify.

4 A parameter / 3 pts

Find the value of \(k\) for which \(x^2-10x+k=0\) has exactly one solution, then give that solution.

5 A poster / 3 pts

A rectangular poster is 6 inches longer than it is wide, and its area is 187 square inches. Find its dimensions.

6 Line and parabola / 3 pts

Solve the system \(y=x^2-1\) and \(y=x+1\).