Evaluating Quadratic Functions and Transformations

The video tutorial explains how to calculate function values for a quadratic function f(x) = -2x^2 - 3x + 7. It covers the calculations for f(0), f(3), and f(-3), demonstrating how to substitute values and simplify using order of operations. The tutorial also explores transformations, including the reflection of f(x) across the y-axis to find f(-x) and the horizontal shift to find f(x+2). Each calculation is linked to its graphical representation, illustrating how these transformations affect the graph of the function.

What is the value of f(0) for the function f(x) = -2x^2 - 3x + 7?

• 0

• 3

• 7

• -7

If f(3) is calculated for the function f(x) = -2x^2 - 3x + 7, what is the result?

• -27

• 20

• 7

• -20

Which point would represent f(3) on the graph of the function f(x) = -2x^2 - 3x + 7?

• (0, 7)

• (3, -20)

• (3, 7)

• (3, 20)

What is the value of f(-3) for the function f(x) = -2x^2 - 3x + 7?

• -9

• 2

• 9

• -2

Which point would represent f(-3) on the graph of the function f(x) = -2x^2 - 3x + 7?

• (3, -2)

• (0, 7)

• (-3, 2)

• (-3, -2)

What transformation does f(-x) represent for the function f(x) = -2x^2 - 3x + 7?

• Translation up

• Translation down

• Reflection across the y-axis

• Reflection across the x-axis

What is the expression for f(-x) if f(x) = -2x^2 - 3x + 7?

• -2x^2 + 3x + 7

• -2x^2 - 3x + 7

• 2x^2 - 3x + 7

• 2x^2 + 3x + 7

What transformation does f(x+2) represent for the function f(x) = -2x^2 - 3x + 7?

• Shift down 2 units

• Shift left 2 units

• Shift right 2 units

• Shift up 2 units

What is the simplified expression for f(x+2) if f(x) = -2x^2 - 3x + 7?

• -2x^2 - 11x - 7

• -2x^2 + 11x + 7

• -2x^2 + 11x - 7

• -2x^2 - 11x + 7

What is the first step in simplifying f(x+2) for the function f(x) = -2x^2 - 3x + 7?

• Multiply by -2

• Add 7

• Subtract 3

• Square x+2