QUADRATIC FORMULA WORKSHEET 

Problem 1-4 : Solve the quadratic equation using the quadratic formula.

Problem 1 :

2x² – 5x + 2 = 0

Problem 2 :

√2f² - 6f + 3√2 = 0

Problem 3 :

3y² - 20y - 23 = 0

Problem 4 :

36y² - 12ay + (a² - b²) = 0

Problem 5 :

A ball rolls down a slope and travels a distance d = t² - 0.75t feet in t seconds. Find the time when the distance traveled by the ball is 11.25 feet.

Answers

1. Answer :

Comparing ax² + bx + c = 0 and 2x² – 5x + 2 = 0, we get

a = 2, b = -5, c = 2

Quadratic Formula :

Substitute a = 2, b = -5 and c = 2.

2. Answer :

√2f² - 6f + 3√2 = 0

From the quadratic equation above,

a = √2, b = -6, c = 3√2

Substitute the above values into the quadratic formula.

3. Answer :

3y² - 20y - 23 = 0

From the quadratic equation above,

a = 3, b = -20, c = -23

Substitute the above values into the quadratic formula.

4. Answer :

36y² - 12ay + (a² - b²) = 0

From the quadratic equation above,

a = 36, b = -12a, c = a² - b²

Substitute the above values into the quadratic formula.

5. Answer :

d = t² - 0.75t

We have to find the time when the distance traveled by the ball is 11.25 feet.

Substitute d = 11.25 into the above equation and solve for t.

11.25 = t² - 0.75t

t² - 0.75t - 11.25 = 0

Multiply both sides by 100 to get rid of the decimal point.

100(t² - 0.75t - 11.25) = 100(0)

100t² - 75t - 1125 = 0

Divide both sides by 25.

4t² - 3t - 45 = 0

From the quadratic equation above,

a = 4, b = -3, c = -45

Substitute the above values into the quadratic formula.

t = 3.75  or  -3

Time can never be a negative value. So, t = -3 can be rejected.

Therefore, 

t = 3.75 seconds

The ball takes 3.75 seconds to travel a distance of 11.25 feet.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.