source : sparknotes.com
Quadratics: Graphing Parabolas | SparkNotes
Graphing y = x2
We have already discovered how to graph linear functions. But what does the graph of y = x2 look like? To find the answer, make a data table:
Data Table for y = x2
And graph the points, connecting them with a smooth curve: Graph of y = x2
The shape of this graph is a parabola.
Note that the parabola does not have a constant slope. In fact, as x increases by 1, starting with x = 0, y increases by 1, 3, 5, 7, . As x decreases by 1, starting with x = 0, y again increases by 1, 3, 5, 7, .
Graphing y = (x – h)2 + k
In the graph of y = x2, the point (0, 0) is called the vertex. The vertex is the minimum point in a parabola that opens upward. In a parabola that opens downward, the vertex is the maximum point.
We can graph a parabola with a different vertex. Observe the graph of y = x2 + 3:
Graph of y = x2 + 3
The graph is shifted up 3 units from the graph of y = x2, and the vertex is (0, 3).
Observe the graph of y = x2 – 3:
Graph of y = x2 – 3
The graph is shifted down 3 units from the graph of y = x2, and the vertex is (0, – 3).
We can also shift the vertex left and right. Observe the graph of y = (x + 3)2:
Graph of y = (x + 3)2
The graph is shifted left3 units from the graph of y = x2, and the vertex is (- 3, 0).
Observe the graph of y = (x – 3)2:
Graph of y = (x – 3)2
The graph is shifted to the right3 units from the graph of y = x2, and the vertex is (3, 0).
In general, the vertex of the graph of y = (x – h)2 + k is (h, k). For example, the vertex of y = (x – 2)2 + 1 is (2, 1):
Graph of y = (x – 2)2 + 1
Desmos | Beautiful, Free Math – Desmos offers best-in-class calculators, digital math activities, and curriculum to help every student love math and love learning math.2x-2y=4 Geometric figure: Straight Line Slope = 1 x-intercept = 2/1 = 2.00000 y-intercept = 2/-1 = -2.00000 Rearrange: Rearrange the equation by subtracting what is to the right of theFunction Grapher is a full featured Graphing Utility that supports graphing up to 5 functions together. You can also save your work as a URL (website link). Usage To plot a function just type it into the function box. Use "x" as the variable like this:
Solve x-2y=4 | Microsoft Math Solver – Algebra Calculator – get free step-by-step solutions for your algebra math problemsGraph y=x-2 y = x − 2 y = x – 2 Use the slope-intercept form to find the slope and y-intercept. Tap for more steps…How do you graph #y=-x-2# using a table? Algebra Graphs of Linear Equations and Functions Applications of Linear Graphs. 1 Answer Nallasivam V Mar 28, 2017 Refer Explanation section. Explanation: Given – #y=-x-2# Form a table assigning values to #x# Plot the points on a graph sheet. Join them with a straight line. Answer link. Related questions
Function Grapher and Calculator – MATH – Get the free "Surface plot of f(x, y)" widget for your website, blog, WordPress, Blogger, or iGoogle. Find more Engineering widgets in Wolfram|Alpha.Summary y = x 2 is a quadratic function, which means its graph is a parabola Quadratic functions have the form y = ax 2 + bx + c Since there is no coefficient in front of the x 2, that means we have an invisible 1Transcribed image text: (1 point) (a) The graph of y = (x – 1)2 + 10 is the graph of y = x2 + 10 shifted horizontally choose the shifting amount and shifted vertically choose the shifting amount (b) The graph of y = x +11 is the graph of y = x + 10 shifted horizontally choose the shifting amount. and shifted vertically choose the shifting amount v. . (c) The graph of y = (x + 5)' – 5(x + 5