Solving Linear-Quadratic Systems Graphically

What is the first step in graphing a quadratic function in a system of equations?

• Calculating the slope

• Finding the y-intercept

• Plotting the vertex

• Determining the x-intercepts

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

• Set x = 0 and solve for y

• Set y = 0 and solve for x

• Calculate the derivative

• Use the quadratic formula

What is the axis of symmetry in the equation y = x^2 + 2x - 8?

• x = 0

• x = 1

• x = 2

• x = -1

What is the vertex of the parabola y = x^2 + 2x - 8?

• (1, -5)

• (-1, -9)

• (0, -8)

• (2, 0)

At which points do the equations y = x^2 + 2x - 8 and y = x - 6 intersect?

• (-2, -8) and (1, -5)

• (0, -8) and (2, 0)

• (-1, -9) and (2, 0)

• (0, -8) and (-1, -9)

In the equation y = -x^2 - 6x - 9, what is the x-coordinate of the vertex?

• -6

• 0

• 3

• -3

What does it mean if a parabolic curve and a horizontal line do not intersect?

• The system has infinite solutions

• The system has two solutions

• The system has one solution

• The system has no solution

What is the significance of the y-intercept in graphing a quadratic equation?

• It indicates the maximum value of the function

• It is used to find the axis of symmetry

• It helps in plotting the initial point of the graph

• It determines the slope of the graph

What are the possible outcomes when a linear and a quadratic function are graphed in a system?

• Always one point of intersection

• Always no intersection

• Two points, one point, or no intersection

• Always two points of intersection

Which of the following is a correct interpretation of a system's graph with no points of intersection?

• The equations are dependent

• The equations have multiple solutions

• The equations are inconsistent

• The equations have one solution