Solving Quadratic Equations by Graphing

This video tutorial covers solving quadratic equations by graphing. It explains the concepts of roots and zeros, and demonstrates how to graph quadratic functions with zero, one, or two solutions. The tutorial also includes practical examples using a graphing calculator and provides insights into analyzing graphs for solutions. The video concludes with additional resources for further learning.

What is the first step in finding the x-intercepts of a quadratic function?

• Set y equal to zero

• Find the vertex

• Set x equal to zero

• Find the axis of symmetry

How many times does a parabola with zero roots cross the x-axis?

• Two times

• One time

• Zero times

• Three times

If a quadratic equation has one root, how many times does its graph touch the x-axis?

• Three times

• Two times

• One time

• Zero times

What is the solution to the quadratic equation x^2 + 4x + 4 = 0?

• x = -4

• x = 4

• x = 2

• x = -2

In the example of a quadratic equation with two roots, what are the roots of the equation x^2 - x - 2 = 0?

• x = -2 and x = 1

• x = -1 and x = 2

• x = 1 and x = 2

• x = -1 and x = -2

What is the axis of symmetry for the quadratic function f(x) = x^2 - 2x - 8?

• x = 2

• x = -2

• x = 1

• x = -1

What is the vertex of the quadratic function f(x) = x^2 - 2x - 8?

• (1, -9)

• (1, 9)

• (-1, 9)

• (-1, -9)

For the quadratic function f(x) = -x^2 + 6x - 9, what is the y-coordinate of the vertex?

• 3

• 6

• 0

• 9

What is the range of the quadratic function f(x) = -x^2 + 6x - 9?

• y ≤ 0

• y ≥ 1

• y ≥ 0

• y ≤ 1

If a quadratic function has no real roots, what can be said about its graph?

• It touches the x-axis at one point

• It does not touch the x-axis

• It touches the x-axis at two points

• It touches the y-axis at one point