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The quadratic formula worksheets Grade 9

Solve quadratic equations with the quadratic formula and simplify the answer.

The front of the free the quadratic formula worksheet
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Free · Worked example · 8 problems · Answer key · US Letter

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How to do it

x = (−b ± √(b² − 4ac)) ÷ 2a. Simplify the radical and reduce.

2x2−6x−1=0x=3±1122x^{2} - 6x - 1 = 0\quad x = \dfrac{3 \pm \sqrt{11}}{2}
a =2,b=−6,c=−1\text{a }= 2,\quad b = -6,\quad c = -1
(−6)2−4(2)(−1)=44(-6)^{2} - 4(2)(-1) = 44the discriminant b² − 4ac
x=6±444x = \dfrac{6 \pm \sqrt{44}}{4}x = (−b ± √(b² − 4ac)) ÷ 2a
x=6±2114x = \dfrac{6 \pm 2\sqrt{11}}{4}√44 = 2√11
x=3±112x = \dfrac{3 \pm \sqrt{11}}{2}simplify

Example problems

  1. x2−x−4=0x^{2} - x - 4 = 0
  2. x2+7x−7=0x^{2} + 7x - 7 = 0
  3. 4x2+7x−2=04x^{2} + 7x - 2 = 0
  4. 4x2+8x−5=04x^{2} + 8x - 5 = 0

Radicals, quadratics and rational expressions

  1. Simplifying square roots
  2. Adding and multiplying radicals
  3. Solving quadratic equations by factoring
  4. Completing the square
  5. The quadratic formula
  6. Simplifying rational expressions
  7. Multiplying and dividing rational expressions