Exploring Quadratic Functions in Vertex Form

What is the general form of a quadratic function in vertex form?

• f(x) = a(x - h)^2 + k

• f(x) = a(x - h)^2 - k

• f(x) = a(x - h) + k

• f(x) = a(x + h)^2 + k

In the equation f(x) = a(x - h)^2 + k, what does the 'h' value represent?

• The direction of the graph

• The vertical shift

• The horizontal shift

• The width of the graph

Given the equation f(x) = (x + 2)^2 - 3, what is the vertex?

• (-2, 3)

• (2, 3)

• (2, -3)

• (-2, -3)

For the equation f(x) = -2(x - 5)^2 + 13, what is the axis of symmetry?

• x = 5

• x = -5

• y = -2

• y = 13

If the 'a' value in a quadratic function is negative, what does this indicate about the graph?

• The graph is narrower

• The graph opens downwards

• The graph opens upwards

• The graph is wider

How do you determine if a quadratic graph is wider or narrower than the parent function?

• By the sign of 'a'

• By the value of 'h'

• By the absolute value of 'a'

• By the value of 'k'

What is the first step in graphing a quadratic function in vertex form?

• Compare the width to the parent function

• Find the vertex

• Identify the axis of symmetry

• Determine the direction of the graph

Given a graph with a vertex at (3, 4) and no 'a' value provided, what is the equation of the quadratic function?

• f(x) = (x - 3)^2 + 4

• f(x) = (x + 3)^2 + 4

• f(x) = (x - 3)^2 - 4

• f(x) = (x + 3)^2 - 4

If a quadratic function has a vertex at (-2, -7) and passes through the point (-3, -9), what is the 'a' value?

• -1

• 1

• 2

• -2

In the context of a real-world problem, if a baseball hit follows the path f(x) = -0.0014(x - 200)^2 + 60, will it be a home run if the Green Monster is 37 feet tall and 310 feet from home plate?

• No, because the ball is only 20 feet high at 310 feet

• No, because the ball is only 30 feet high at 310 feet

• Yes, because the ball is 43.06 feet high at 310 feet

• Yes, because the ball is 37 feet high at 310 feet