Verifying Quadratic Equations Graphically

The video tutorial explains the process of completing the square in quadratic equations. It begins with an introduction to constants and the importance of isolating them. The tutorial then covers adjusting the coefficient of X squared to one by dividing all terms. It explains perfect squares and how to factor them, followed by solving the equation for X. Finally, it demonstrates using Desmos to verify solutions graphically, ensuring the solutions are correct.

What is the first step in completing the square?

• Divide all terms by the coefficient of x squared.

• Solve for x using the quadratic formula.

• Find the perfect square trinomial.

• Move the constant to the other side of the equation.

Why do we divide all terms by the coefficient of x squared?

• To make the equation easier to solve.

• To eliminate the constant term.

• To ensure the coefficient of x squared is one.

• To find the roots of the equation.

What is a perfect square trinomial?

• A quadratic equation with a constant term.

• A polynomial with three terms.

• An equation with no real solutions.

• An expression that can be factored into a binomial squared.

How do you determine the value of b in a perfect square trinomial?

• By solving the equation for x.

• By dividing the middle term by two.

• By using the quadratic formula.

• By factoring the trinomial.

What must be done after adding a value to complete the square on one side of the equation?

• Divide the equation by the constant term.

• Subtract the same value from the other side.

• Add the same value to the other side.

• Multiply the equation by the coefficient of x squared.

What is the result of factoring the expression (x + 5)^2?

• x^2 + 10x + 25

• x^2 + 10x

• x^2 + 5x + 10

• x^2 + 25

What are the possible solutions for x when solving the equation after completing the square?

• Only positive values.

• No solutions.

• Both positive and negative values.

• Only negative values.

How can you verify the solutions of a quadratic equation graphically?

• By checking the y-intercept.

• By finding the vertex of the parabola.

• By observing where the graph crosses the x-axis.

• By calculating the slope of the tangent.

What is the significance of the values where the parabola crosses the x-axis?

• They show the rate of change of the function.

• They represent the maximum and minimum points.

• They are the solutions to the quadratic equation.

• They indicate the symmetry of the graph.

Which tool was suggested for verifying the solutions graphically?

• Khan Academy

• GeoGebra

• Wolfram Alpha

• Desmos