Inverse Functions and Quadratics

The video tutorial covers various mathematical concepts, including transformations of quadratic functions, finding inverses of exponential and linear functions, understanding the standard form of a circle, calculating compound interest, using synthetic division for polynomials, identifying vertical asymptotes, solving work rate problems, and properties of inscribed triangles. Each section provides step-by-step explanations and examples to help students grasp these concepts effectively.

What does the leading negative sign in a quadratic function indicate?

• Reflection over the y-axis

• Reflection over the x-axis

• Horizontal shift

• Vertical stretch

What transformation occurs when a quadratic function is vertically stretched by a factor of two?

• The parabola shifts up

• The parabola gets narrower

• The parabola gets wider

• The parabola shifts down

What is the inverse of an exponential function?

• Polynomial function

• Logarithmic function

• Linear function

• Quadratic function

What is the first step in finding the inverse of an exponential function?

• Convert to logarithmic form

• Switch x and y

• Isolate the exponential part

• Subtract any constants

How do you find the value of the inverse of a linear function?

• Plug the value into y and solve for x

• Switch x and y and solve for x

• Switch x and y and solve for y

• Plug the value into x and solve for y

What is the standard form of a circle?

• x - h^2 + y - k^2 = r^2

• x^2 + y^2 = r^2

• x - h^2 + y - k^2 = r^2

• x - h^2 + y - k^2 = r

What is the center of the circle given by the equation (x - 3)^2 + (y + 8)^2 = 121?

• (3, 8)

• (-3, -8)

• (3, -8)

• (-3, 8)

What is the formula for compounded interest?

• A = P(1 + rt)

• A = P(1 - r/n)^(nt)

• A = P(1 + r/n)^(nt)

• A = P(1 + r/n)^(t/n)

What is the remainder when the polynomial x^3 - 10x + 17 is divided by x - 1?

• 8

• 10

• 26

• 17

What is the measure of angle P in a triangle inscribed in a circle with one side as the diameter?

• 45 degrees

• 120 degrees

• 60 degrees

• 90 degrees