Quadratic Formula
Write the quadratic equation in standard form:
-3x2 - 3x - 9 = - 2
-3x2 - 3x -7 = 0
Solve by completing the square:
x2+5x+6=0
x=−2,−3
Factor:
x2+7x+12=0
x=−3,−4
Solve:
3x−5>10
x>5
Complete the square:
x2+6x+9
(x+3)2
Find the solution for:
x2+7x+12=0
x=−3 x=−4
solve by completing the square:
2x2+3x−2=0
x=1/2,−2
Factor:
x2−4x−12=0
x=6,−2
Graph on a number line:
x−3≤2
x≤5
Rewrite in standard form:
(x+2)(x−5)=0
x2−3x−10=0
Rewrite in standard form:
(x−4)(x+1)=7
x2−3x−11=0
Solve this by completing the square:
x2+4x−1=0
x=−2±5
Factor:
2x2+8x=0
x=0,−4
Graph the system of inequalities and give one solution:
y > x-2
y ≤ 4
(2,3)
A quadratic has solutions x=3 and x=−4. Write it in standard form.
(x−3)(x+4)=0 → x2+x−12
Find the solution for:
3x2−12x=0
x=0,4
Complete the square and solve:
x2−8x+7=0
x=1,7
Factor:
2x2+7x+3
(2x+1)(x+3)
x= -3, -1/2
Graph the system of inequalities and give one solution:
y≥−x+1
y<5
(1,2)
Solve by any method:
x2−12x+20=0
x=10,2
One solution to a quadratic equation is x=5. The other is x=−2. Write a quadratic equation in standard form.
Step 1: (x−5)(x+2)=0
Final answer: x2−3x−10=0
Complete the square and solve:
x2−12x+11=0
x=1,11
Factor:
3x2−14x−5
(3x+1)(x−5)
x=5, -1/3
Solve and graph the solution:
3(2x−5)+7≤4x+19
x≤13.5
A quadratic equation has one solution repeated. It can be written as:
(x−6)2=0
What is the solution?
Write it in standard form.
Solution: x=6x=6x=6
Standard form: x2−12x+36=0