Quadratic Word Problems by Factoring

• Set the input equal to 1 and solve.

• Set the output equal to 1 and solve by factoring.

• Find the x-intercept by setting the equation equal to zero and solve by factoring or quadratic formula.

• Find the y-intercept by setting the input equal to zero and solve.

What is the first step in solving 
(x + 2)(x - 3) = 0      ?

• Plug in zero for x

• Solve for x

• FOIL

• Set each binomial factor equal to zero

Tags

CCSS.HSA-REI.B.4B

Step 1: Factor out GCF 0 = -5(t² + 20t + 60) Step 2: Since the GCF is just a number and not a number with a variable, we can divide both sides by it to obtain: 0 = ( t² - 4t - 12 ) Step 3: Factor the quadratic. 0 = ( t-6)(t+2) Step 4: Set each factor to zero. t-6 = 0 and t +2 = 0 t = 6 and t = -2 7. Since this is a word problem, which answer should we exclude?

• None, both answers work!

• t = -2 because time cannot be negative.

• t = 6 because it is extraneous

• Both answers, because neither answer works in the equation.

Tags

CCSS.HSA-REI.B.4B

A frog is sitting on the ground when he is scared by a big dog. His movement is modeled by the equation h = -6t² + 6t where h is the frog's height at any given time, t . How many seconds until the frog is back on the ground?

*Hint: For this problem, the concept is the same, but the factoring method has changed to GCF only.

• 0.5 seconds

• 1 second

• 1.5 seconds

• 2 seconds

• 3 seconds

• 7 ft

• 16 ft

• 8 ft

• 14 ft

The sum of a number and its square is 72. Find the number(s).

• 8 or 9

• 8 or -9

• -8 or 9

• -8 or -9

Tags

CCSS.8.EE.A.2

Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds. When is the ball at ground level? *Hint: For this problem, the concept is the same, but the factoring method for this one has changed to GCF and Difference of Squares.

• only at t = 0 seconds

• only at t = 3 seconds

• only at t = 9 seconds

• at both t = 0 seconds and t = 3 seconds

Tags

CCSS.HSA-REI.B.4B

Here is a word problem: "The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?" Since f(t) = 0 at the ground, sub a zero in for f(t). 4. What equation do you get when you make that substitution?

• 0 = -5t²+20t + 60

• f(0) = -5(0)²+20(0)+ 60

If you square 5 more than a positive number, the result is 88 more than 12 times the number.  Find the numbers.

• -9, 7

• √75

• 9, -7

• 15, -5