F25 Lesson 7.7 Quadratic Equations and Problem Solving

​The square of a number plus three times the number is 70. Find the number.

Open Ended

The square of a number plus three times the number is 70. Find the number.

Fill in the Blanks

When 21 is subtracted from the square of a number, the result is 4 times the number. Find the negative solution.

Fill in the Blanks

The difference of the square of a number and 21 is equal to 4 times that number. Find the negative solution.

Multiple Choice

If x is one of the unknown positive integers, what is the expression for the next consecutive positive integer?

• x+2

• x-1

• x+1

• 2x

Multiple Choice

Which of the following equations correctly translates the statement: 'The product of two consecutive positive integers is 132'?

• x(x+1)=132

• x(x-1)=132

• x^2=132

• x+1=132

Fill in the Blanks

Fill in the blank: The quadratic equation formed from the product of two consecutive positive integers being 132 is x^2 + x -

= 0.

Open Ended

Why is x = -12 not considered a valid solution for the problem of finding two consecutive positive integers whose product is 132?

Open Ended

The product of two consecutive positive integers is 132. Find the two integers.

Open Ended

Find two consecutive even numbers such that the sum of the smaller number and twice the greater number is 100.

Open Ended

The height, h, in feet of a golf ball after t seconds is given by h = -16t^2 + 96 t. Find how long it takes the golf ball to return to the ground.

Open Ended

The height of a triangular sail is 2 meters less than twice the length of the base. If the sail has an area of 30 square meters, find the length of its base and the height.

Multiple Choice

Which formula is used to find the length of the hypotenuse in a right triangle?

• a^2 + b^2 = c^2

• a^2 - b^2 = c^2

• a^2 + b^2 = 2c^2

• a^2 + c^2 = b^2

Open Ended

Find the length of the shorter leg of a right triangle if the longer leg is 10 miles more than the shorter leg and the hypotenuse is 10 miles less than twice the shorter leg.

Fill in the Blanks

The equation x^2 + 3x - 68 = 3x - 4 can be rewritten as x^2 +

= 0. Fill in the blank.