Understanding Quadratic Equations and Their Solutions

The video tutorial explains how to solve the equation f(x) = x^2 - x for f(x) = 6. It involves substituting the function into the equation, simplifying it to a quadratic form, and then factoring it to find the x values that satisfy the equation. The solutions are verified graphically by plotting the function and the constant line f(x) = 6, showing their points of intersection.

What is the function given in the problem?

• f(x) = x^2 + x

• f(x) = x^2 - x

• f(x) = x^2 - 2x

• f(x) = x^2 + 2x

What is the value of f(x) we need to solve for?

• f(x) = 0

• f(x) = -6

• f(x) = 6

• f(x) = 3

What equation do we get after substituting and simplifying the function?

• x^2 + x = 6

• x^2 - x = 0

• x^2 - x = 6

• x^2 + x = 0

What is the next step after forming the equation x^2 - x = 6?

• Add 6 to both sides

• Subtract 6 from both sides

• Divide both sides by 6

• Multiply both sides by 6

What are the factors of the quadratic equation x^2 - x - 6 = 0?

• (x - 2)(x + 3)

• (x - 3)(x + 2)

• (x + 3)(x + 2)

• (x - 3)(x - 2)

What are the solutions for x after factoring the equation?

• x = 2 and x = -3

• x = 3 and x = -2

• x = -2 and x = 3

• x = -3 and x = 2

How can we verify the solutions graphically?

• By plotting the function and checking for intersections with the y-axis

• By plotting the function and checking for intersections with the x-axis

• By plotting the function and checking for intersections with the line y = 0

• By plotting the function and checking for intersections with the line y = 6

What are the points of intersection when verifying graphically?

• (-2, 0) and (3, 0)

• (2, 0) and (-3, 0)

• (-2, 6) and (3, 6)

• (2, 6) and (-3, 6)

What does the point (-2, 6) on the graph indicate?

• f(-2) = 0

• f(-2) = 3

• f(-2) = 6

• f(-2) = -6

What does the point (3, 6) on the graph indicate?

• f(3) = 6

• f(3) = 3

• f(3) = 0

• f(3) = -6