Graphing Quadratics in Vertex Form

The video tutorial introduces the vertex form of quadratic equations, explaining how to identify the vertex directly from the equation. It provides a step-by-step guide to graphing quadratic equations using vertex form, including plotting the vertex and additional points. Two examples are given: one with a positive quadratic equation and another with a negative quadratic equation, demonstrating the process of graphing each and highlighting the differences in their parabolic shapes.

What is the vertex form of a quadratic equation?

• y = ax^2 + bx + c

• y = a(x - h)^2 + k

• y = a(x + h)^2 + k

• y = a(x - h)^2 - k

In the vertex form y = a(x - h)^2 + k, what do 'h' and 'k' represent?

• The vertex coordinates

• The roots of the equation

• The x-intercept and y-intercept

• The coefficients of x

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

• Calculate the y-intercept

• Identify and plot the vertex

• Find the roots

• Determine the axis of symmetry

For the equation y = (x - 1)^2 + 2, what is the vertex?

• (-1, -2)

• (1, -2)

• (-1, 2)

• (1, 2)

How do you determine the next points to plot after the vertex?

• By finding the roots

• By using the value of 'a' to go out and up/down

• By calculating the y-intercept

• By determining the axis of symmetry

For the equation y = (x - 1)^2 + 2, what are the y-values for x = 0 and x = 2?

• 4 and 2

• 3 and 3

• 2 and 4

• 1 and 3

What shape does the graph of a quadratic equation form?

• An ellipse

• A straight line

• A circle

• A parabola

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

• (-2, -3)

• (2, 3)

• (-2, 3)

• (2, -3)

How does a negative 'a' value affect the graph of a quadratic equation?

• It shifts the graph to the right

• It shifts the graph to the left

• It makes the graph open downwards

• It makes the graph open upwards

For the equation y = -2(x + 2)^2 - 3, what is the y-value when x = 0?

• -7

• -11

• -3

• -5