Understanding Quadratic Graphs

This video tutorial by Mr. Backer covers graphing quadratic equations, focusing on the general form y = ax^2 + bx + c. It explains how the 'a' value affects the parabola's orientation and width, and how to find the vertex and axis of symmetry using the equation. The tutorial includes step-by-step examples to illustrate these concepts, showing how to graph parabolas by identifying key points and plotting them. The video concludes with practical examples to reinforce the learning objectives.

What happens to the parabola if the coefficient 'a' is negative?

• The parabola becomes narrower.

• The parabola opens downwards.

• The parabola opens upwards.

• The parabola becomes wider.

How do you determine the axis of symmetry for a quadratic equation?

• By finding the highest point on the graph.

• By finding the y-intercept.

• By using the formula x = -b/2a.

• By setting the equation to zero.

In the equation y = x^2 - 2x - 3, what is the value of 'b'?

• -3

• -2

• 1

• 3

For the equation y = x^2 - 2x - 3, what is the x-coordinate of the vertex?

• -1

• 1

• 0

• 2

In the equation y = 2x^2 + 12x - 7, what is the value of 'a'?

• 2

• -7

• 12

• 1

What is the axis of symmetry for the equation y = 2x^2 + 12x - 7?

• x = 6

• x = -3

• x = 3

• x = -6

What is the first step in graphing a parabola?

• Identify the x-intercepts.

• Calculate the slope.

• Determine the axis of symmetry.

• Find the y-intercept.

For the equation y = x^2 + 4x - 3, what is the axis of symmetry?

• x = 4

• x = -4

• x = 2

• x = -2

In graphing a parabola, why is it important to find points on both sides of the vertex?

• To ensure the graph is symmetrical.

• To find the y-intercept.

• To calculate the area under the curve.

• To determine the slope of the line.

What shape does a parabola typically have?

• A zigzag

• A straight line

• A circle

• A U-shape