Writing Equations of Polynomials Using X-Intercepts

This video tutorial teaches how to write polynomial equations by analyzing x-intercepts. It covers graph reflection over the x-axis, understanding zeros, and common misunderstandings about factored form. The tutorial demonstrates forming equations from graph x-intercepts, simplifying them, and handling advanced examples with multiple x-intercepts and reflections.

What happens to a graph when you multiply its function by negative 1?

• It reflects over the x-axis.

• It shifts to the right.

• It shifts upwards.

• It becomes a horizontal line.

Where do the zeros of a function occur on a graph?

• Where the graph is at its lowest point.

• Where the graph is at its highest point.

• Where the graph crosses the x-axis.

• Where the graph crosses the y-axis.

If (7, 0) is an x-intercept, what is the correct factor form?

• x / 7

• x + 7

• x - 7

• x * 7

What is the result of multiplying any number by zero?

• One.

• Zero.

• The number itself.

• Infinity.

How do you form a polynomial equation from x-intercepts?

• Subtract the x-intercepts from each other.

• Add the x-intercepts together.

• Divide the x-intercepts by each other.

• Multiply the factors derived from x-intercepts.

How can you handle a fractional x-intercept like 1/2?

• Ignore the fraction.

• Multiply both sides by the denominator.

• Add the fraction to the equation.

• Divide the equation by the fraction.

What is the effect of reflecting a graph over the x-axis?

• It inverts the graph vertically.

• It compresses the graph vertically.

• It stretches the graph horizontally.

• It shifts the graph to the left.