Graphing Quadratic Functions: Key Parts and Vertex Form

Mr. Allen introduces graphing quadratic functions in vertex form, focusing on identifying key features such as the vertex and axis of symmetry. He demonstrates how to plot points using symmetry and calculates the y-intercept. The video concludes with solving for x-intercepts, providing a comprehensive guide to graphing quadratics.

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

• y = ax^2 + k

• y = a(x + h)^2 + k

• y = ax^2 + bx + c

• y = a(x - h)^2 + k

In the function g(x) = -2(x - 3)^2 + 4, what is the vertex?

• (-3, -4)

• (3, -4)

• (-3, 4)

• (3, 4)

What is the axis of symmetry for the function g(x) = -2(x - 3)^2 + 4?

• x = -3

• x = -4

• x = 4

• x = 3

If you have a point (2, 2) on the graph, what is its reflection over the axis of symmetry x = 3?

• (3, 2)

• (4, 4)

• (2, 4)

• (4, 2)

How do you find the y-intercept of a quadratic function in vertex form?

• Set x to 0 and solve for y

• Set y to 0 and solve for x

• Use the vertex coordinates

• Use the axis of symmetry

What is the y-intercept of the function g(x) = -2(x - 3)^2 + 4?

• (0, 14)

• (0, -4)

• (0, -14)

• (0, 4)

What is the first step in solving for the x-intercepts of the function g(x) = -2(x - 3)^2 + 4?

• Add 4 to both sides

• Subtract 4 from both sides

• Divide both sides by -2

• Multiply both sides by -2

After subtracting 4 and dividing by -2, what equation do you get for finding the x-intercepts?

• x + 3 = ±2

• x - 3 = ±2

• x + 3 = ±√2

• x - 3 = ±√2

What are the x-intercepts of the function g(x) = -2(x - 3)^2 + 4?

• (3 ± √2, 0)

• (3 ± 2, 0)

• (3 ± √3, 0)

• (3 ± 1.4, 0)

Which of the following is NOT typically asked when graphing a quadratic function in vertex form?

• Vertex

• Axis of Symmetry

• X-Intercept

• Y-Intercept