Quadratic Functions and Their Properties

The video tutorial explains how to find the x and y intercepts of a quadratic function. It begins by setting the function equal to zero to find the x intercepts using the quadratic formula. The solution is simplified, and the intercepts are verified graphically with decimal approximations. The y intercept is found by setting x to zero, and the graph is used to confirm all intercepts.

What is the first step in finding the x-intercepts of a quadratic function?

• Set y or f(x) equal to zero and solve for x

• Set x equal to zero and solve for y

• Use the quadratic formula directly

• Graph the function and find the intercepts visually

Which of the following represents the correct coefficients for the quadratic formula in the equation x^2 + 2x - 9?

• a = 1, b = 2, c = 9

• a = 1, b = -2, c = -9

• a = 1, b = 2, c = -9

• a = 2, b = 1, c = -9

What is the discriminant of the quadratic equation x^2 + 2x - 9?

• 36

• 40

• 4

• 44

How do you simplify the expression -2 ± 2√10 divided by 2?

• -1 ± √10

• -2 ± 2√10

• -1 ± 2√10

• -2 ± √10

What is the approximate decimal value of -1 - √10?

• -3.16

• -4.16

• -5.16

• -2.16

Why is it important to use decimal approximations when checking intercepts graphically?

• To ensure the graph is drawn to scale

• To make calculations easier

• To verify the intercepts are correct

• To avoid using exact values

What is the y-intercept of the function f(x) = x^2 + 2x - 9?

• (0, -9)

• (9, 0)

• (-9, 0)

• (0, 9)

How can you quickly identify the y-intercept from the quadratic equation in standard form?

• By looking at the constant term

• By finding the vertex

• By solving for x

• By setting x to zero

What is the graphical representation of the smaller x-intercept?

• Approximately (2.16, 0)

• Approximately (-4.16, 0)

• Approximately (-2.16, 0)

• Approximately (4.16, 0)

Which of the following is true about the x-intercepts of the function f(x) = x^2 + 2x - 9?

• They are both zero

• They are both positive

• They are both negative

• One is positive and one is negative