Solving Quadratics with Desmos

The video tutorial introduces solving quadratic equations by graphing, using Desmos as a tool. It covers key terms like zeros, roots, and x-intercepts, and demonstrates the process of setting equations to zero and identifying solutions through graphing. Example problems are solved to illustrate the method, and the concept of real and imaginary solutions is discussed.

What is the primary tool used for graphing in this lesson?

• A scientific calculator

• Desmos

• A graphing paper

• Microsoft Excel

What are the zeros of a function also known as?

• Coefficients

• Derivatives

• Vertices

• Roots

What is the first step in solving quadratic equations as discussed?

• Setting the equation to zero

• Finding the derivative

• Factoring the equation

• Graphing the equation

How can Desmos help in solving quadratic equations?

• By providing the equation's derivative

• By solving for x directly

• By identifying the x-intercepts

• By automatically factoring equations

What is the significance of setting a quadratic equation to zero?

• It helps in identifying the equation's maximum value

• It is necessary for finding the derivative

• It simplifies the equation for graphing

• It is the standard first step in various solving methods

What were the zeros found for the equation y = x^2 - 4x - 2?

• 0 and -2

• -0.449 and 4.449

• -1 and 1

• 2 and -2

After adjusting the equation 2x^2 + 8x = 10, what is the new form?

• 2x^2 + 8x + 10 = 0

• 2x^2 + 8x - 10 = 0

• 2x^2 - 8x + 10 = 0

• x^2 + 4x - 5 = 0

What are the solutions for the equation 2x^2 + 8x - 10 = 0?

• x = 2 and x = -5

• x = -5 and x = 1

• x = 5 and x = -1

• x = 0 and x = 10

What does it mean if a parabola does not touch the x-axis?

• It is not a function

• It has no real solutions

• It has one real solution

• It has two real solutions

What indicates no real solutions in Desmos?

• A straight line

• A parabola not crossing the x-axis

• A dotted line

• A parabola touching the x-axis