Solving Quadratic Equations by Inspection

The video tutorial explains how to solve quadratic equations by inspection, starting with a review of perfect squares. It highlights that perfect squares have both positive and negative factors that multiply to the same number. The tutorial then demonstrates solving quadratic equations by inspection, using examples like X^2 = 49 and X^2 = 100, showing that both positive and negative roots are solutions. It also explains why some equations, like X^2 = -100, have no solutions. The video concludes with a graphical interpretation of quadratic solutions as points where the parabola crosses the x-axis.

What is a perfect square?

• A number that can be divided by 2

• A number that is a multiple of 10

• A number with two identical factors

• A number that is always positive

Which of the following is a solution to the equation X^2 = 49?

• 5

• 8

• 6

• 7

What does the graph of a quadratic equation typically look like?

• A parabola

• A hyperbola

• A circle

• A straight line

Why does the equation X^2 = -100 have no solutions?

• Because 100 is not a perfect square

• Because no number multiplied by itself can be negative

• Because -100 is not a real number

• Because the equation is not quadratic

What are the solutions to the equation X^2 = 100?

• 10 and -10

• 15 and -15

• 5 and -5

• 20 and -20