Students understand that the number of zeros in a polynomial function corresponds to the number of linear factors of the related expression and that different functions may have the same zeros but different maxima or minima.

New York State Common Core Math Module 4, Algebra I, Lesson 9Related Topics:

Lesson Plans and Worksheets for Algebra I

Lesson Plans and Worksheets for all Grades

More Lessons for Algebra I

Common Core For Algebra I

Lesson 9 Summary

When we have a quadratic function in factored form, we can find its x-intercepts, y-intercept, axis of symmetry, and vertex.

For any quadratic equation, the roots are the solution(s) where y = 0, and these solutions correspond to the points where the graph of the equation crosses the x-axis.

A quadratic equation can be written in the form y = a(x - m)(x - n), where m and n are the roots of the quadratic. Since the x-value of the vertex is the average of the x-values of the two roots, we can substitute that value back into equation to find the -xvalue of the vertex. If we set x = 0, we can find the y-intercept.

In order to construct the graph of a unique quadratic function, at least three distinct points of the function must be known.

Examples:

f(x) = x^{2} + x - 30, f(x) = -(x + 2)(x -5)

Find the x-intercepts, y-intercept, axis of symmetry and vertex or turning point.

Lesson 9 Problem Set Sample Solutions

1. Graph the following on your own graph paper and identify the key features of the graph.

a) f(x) = (x - 2)(x + 7)

b) g(x) = -2(x - 2)(x + 7)

c) h(x) = x^{2} - 16

d)
p(x) = x^{2} - 2x + 1

e) q(x) = 4x^{2} - 20x + 24

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.