Common Core (Functions)
Common Core Mathematics
Videos and lessons with examples and solutions to help High School students learn how to graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
Graph linear and quadratic functions and show intercepts, maxima, and minima.
Common Core: HSF-IF.C.7
The following figure shows how to graph a quadratic function in general form. Scroll down the page for more examples and solutions on graphing quadratic functions.
Ex: Graph a Linear Function Using a Table of Values
This video provides and example of how to graph a linear function by completing a table of values.
Graphing Quadratic Functions in General Form or Standard Form
This video explains how to graph quadratic functions in the form f(x) = ax2+ bx + c.
The graph of a quadratic function is called a parabola.
a) It is always a cup-shaped curve.
b) It opens upward if a > 0 or opens downward if a < 0
c) The vertical line x = -b/2a is the line of symmetry.
d) It has a turning point, or vertex, at the point (-b/2a, f(-b/2a)).
Ex1: Graph a Quadratic Function in General Form
This video explains how to determine the x and y intercepts, equation of the axis of symmetry, and the vertex in order to graph a quadratic function. The function is factorable.
** Ex2: Graph a Quadratic Function in General Form**
This video explains how to determine the x and y intercepts, equation of the axis of symmetry, and the vertex in order to graph a quadratic function. The function is NOT factorable.
Given f(x) = -x2 + 4x + 2, find the following and then graph. x-intercepts, y-intercept, equation of axis, vertex.
Graphing Quadratic Functions Using Symmetric Points
This video provides an alternative method for graphing quadratic functions using symmetric points and the vertex.
Graphing Quadratic Functions in Vertex Form
This video explains how to graph quadratic functions in the form f(x) = a(x-h)2 + k.
The vertex of the parabola occurs at the point (h,k), and the vertical line passing through the vertex is the axis of the parabola.
** Quadratic Functions - Find Vertex and Intercepts Using the Graphing Calculator**
This video explains how to find the vertex, y-intercept, and x-intercepts of a quadratic function on the TI-84 graphing calculator.
f(x) = 2x2 - 14x + 7
Find the vertex, the y-intercept or vertical intercept, the x-intercepts or horizontal intercepts.
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
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