Exploring Quadratic Transformations

What is the standard form of a quadratic equation?

• ax^2 + bx + c

• ax + b

• x^2 + bx + c

• ax^2 + bx

What does the 'a' coefficient in the vertex form of a quadratic equation affect?

• Horizontal shifts

• Vertical shifts

• Width and direction of the parabola

• None of the above

If 'h' is positive in the vertex form of a quadratic equation, the graph will shift:

• Left

• Right

• Up

• Down

What effect does a negative 'k' value have on the graph of a quadratic equation?

• Shifts it left

• Shifts it right

• Shifts it up

• Shifts it down

In the equation f(x) = (x + 2)^2 - 3, what is the effect of the '+2' inside the parentheses?

• Shifts down by 2 units

• Shifts up by 2 units

• Shifts left by 2 units

• Shifts right by 2 units

What does a negative coefficient in front of the parentheses in a quadratic equation indicate?

• Horizontal shift

• Narrowing of the graph

• Vertical stretch

• Reflection across the x-axis

How does the graph of the function f(x) = x^2 compare to g(x) = f(x) + 2?

• g(x) is shifted right by 2 units

• g(x) is shifted left by 2 units

• g(x) is shifted down by 2 units

• g(x) is shifted up by 2 units

What is the domain of any quadratic function graphed on a calculator?

• All negative numbers

• 0 to positive infinity

• All positive numbers

• All real numbers

If a quadratic graph starts at y=0 and only increases, what is the range?

• y < 0

• y ≥ 0

• y ≤ 0

• y > 0

What happens to the graph of a quadratic function if you subtract a number from the function?

• Shifts down by the number

• Shifts up by the number

• Shifts right by the number

• Shifts left by the number