Solving Quadratic Equations by Graphing

The video tutorial covers solving quadratic equations by graphing. It includes examples with two real solutions, one real solution, and no real solutions. The process involves setting equations to zero, identifying coefficients, finding the axis of symmetry, and determining the vertex. The tutorial emphasizes graphing techniques to find x-intercepts and verify solutions.

What is the first step in solving the quadratic equation x^2 + 2x = 3 by graphing?

• Set the equation equal to zero

• Find the y-intercept

• Identify the vertex

• Plot the points on the graph

What is the axis of symmetry for the equation x^2 + 2x - 3 = 0?

• x = -2

• x = 1

• x = 2

• x = -1

What is the y-value of the vertex for the equation x^2 + 2x - 3 = 0?

• -4

• -3

• 0

• 4

What are the solutions to the equation x^2 + 2x - 3 = 0?

• x = 1 and x = -3

• x = 3 and x = -1

• x = 1 and x = -1

• x = 3 and x = -3

What is the axis of symmetry for the equation x^2 + 7x + 10 = 0?

• x = 7

• x = -3.5

• x = -7

• x = 3.5

What is the y-value of the vertex for the equation x^2 + 7x + 10 = 0?

• 2.25

• -2.25

• 10

• -10

What is the solution to the equation x^2 - 8x + 16 = 0?

• x = 4

• x = -4

• x = 8

• x = -8

What is the y-value of the vertex for the equation x^2 - 8x + 16 = 0?

• 8

• -4

• 4

• 0

What is the axis of symmetry for the equation -x^2 = 2x + 4?

• x = 2

• x = -2

• x = 1

• x = -1

Why does the equation -x^2 = 2x + 4 have no real solutions?

• The axis of symmetry is positive

• The y-intercept is negative

• The vertex is on the x-axis

• The parabola does not intersect the x-axis