Graph a quadratic equation with vertex and line of symmetry

The video tutorial explains how to graph quadratic equations, focusing on transformations, axis of symmetry, and vertex. It demonstrates how to plot points using symmetry and complete the graph of a quadratic function. The tutorial emphasizes the importance of choosing appropriate values for plotting and understanding the symmetrical nature of parabolas.

What is the main difference between the equations y = x^2 and y = x^2 - 7x + 8?

• The second equation has additional terms that transform the graph.

• The second equation is linear.

• The first equation is a cubic function.

• The second equation is a constant function.

What is the formula for finding the axis of symmetry in a quadratic equation?

• x = 2a / b

• x = a / 2b

• x = b / 2a

• x = -b / 2a

Why is the axis of symmetry important in graphing a quadratic equation?

• It shows where the graph intersects the y-axis.

• It indicates the maximum value of the function.

• It helps in finding the vertex of the parabola.

• It determines the slope of the line.

How do you find the y-value of the vertex in a quadratic equation?

• By calculating the average of the roots.

• By setting x to zero.

• By using the axis of symmetry and substituting it into the equation.

• By finding the derivative of the equation.

What is the vertex of the quadratic equation y = x^2 - 7x + 8?

• (0, 8)

• (3.5, -4.25)

• (7, 0)

• (3.5, 0)

Why is it important to choose points on both sides of the axis of symmetry when plotting a quadratic graph?

• To ensure the graph is a straight line.

• To verify the graph is symmetrical.

• To determine the slope of the graph.

• To find the maximum point of the graph.

What shape does the graph of a quadratic equation typically have?

• A straight line

• A circle

• A U-shaped parabola

• A zigzag pattern