Understanding Quadratic Equations

What is the primary goal when solving a quadratic equation?

• Finding the y-intercepts

• Finding the x-intercepts

• Finding the slope

• Finding the vertex

How many solutions does a quadratic equation typically have when it intersects the x-axis at two points?

• One solution

• Two solutions

• No solution

• Infinite solutions

In the equation x^2 - 16 = 0, what are the solutions?

• 16 and -16

• 0 and 16

• 8 and -8

• 4 and -4

Why does the equation 3x^2 + 6 = 0 have no solutions?

• Because it has an imaginary number

• Because it has a positive under the square root

• Because it has a negative under the square root

• Because it has a zero under the square root

What is the solution for the equation x^2 = 0?

• x = -1

• x = 1

• x = 0

• No solution

For the equation x^2 - 36 = 0, what are the solutions?

• 0 and 36

• 36 and -36

• 12 and -12

• 6 and -6

What happens when you take the square root of a negative number in a quadratic equation?

• You get one solution

• You get a complex number

• You get two solutions

• You get no solutions

What is the general rule for the number of solutions when x^2 equals a positive number?

• Two solutions

• One solution

• No solution

• Infinite solutions

In the final problem, why is the negative solution for the height of the triangle not considered?

• Because it is not a real number

• Because it results in a complex number

• Because it is not a valid solution

• Because height cannot be negative

What is the approximate positive solution for the height in the final problem?

• 5.32 feet

• 6.32 feet

• 7.32 feet

• 8.32 feet