Graph B is the only curve which could be a cubic function. Also the y -intercept is positive on the curve and the equation. Graph A :. All graphs have two turning points so all the graphs could be graphs of cubic functions. So the correct graph is not one of these. But the y intercept on Graph A is negative, and the given equation ends with -3 so this is the correct graph. Graph C : Graph D :. These values give coordinates such as -2,-1 , -1,4 and so on.
These values give coordinates such as -3, , -2,5 and so on. Correct values are: 10, 3 and For 1 correct y -values. Correct values are: 6, 2 and For 1 correct y -value. For answer between 2. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors. Find out more about our GCSE maths revision programme. What is a cubic graph? How to identify a cubic graph. Cubic graph worksheet. Identifying a cubic graph examples.
Example 1: recognising cubic graphs Example 2: recognising cubic graphs. How to plot a cubic graph. Plotting a cubic graph examples. How to use a cubic graph. Using a cubic graph examples. Example 5: use a cubic graph to solve the equation Example 6: use a cubic graph to solve the equation. Common misconceptions. Practice cubic graph questions. Cubic graph GCSE questions. Learning checklist. Next lessons. Still stuck? In order to access this I need to be confident with: Substitution Coordinates Straight line graphs Powers and roots.
This topic is relevant for:. Cubic Graph Here we will learn about cubic graphs , including recognising and sketching cubic graphs. How to identify a cubic graph In order to recognise a cubic graph: Identify linear or quadratic or any other functions. Identify the cubic function checking if the x 3 term is positive or negative.
Graph B is a straight line — it is a linear function Graph D is a parabola — it is a quadratic function. The given equation has a negative x 3 term so the graph will decrease. Graph C is increasing, so Graph C cannot be the correct graph. See also General Function Explorer where you can graph up to three functions of your choice simultaneously using sliders for independent variables as above.
Its graph is therefore a horizontal straight line through the origin. Now move the d slider and let it settle on, say, It is therefore a straight horizontal line through 12 on the y axis. Play with different values of d and observe the result. This is a simple linear equation and so is a straight line whose slope is 2. That is, y increases by 2 every time x increases by one. Quadratic functions are easy to graph because their graphs are always parabolas, so they have the same basic shape.
For higher degree polynomials the situation is more complicated. The applets Cubic and Quartic below generate graphs of degree 3 and degree 4 polynomials respectively. These applets use the fact that 4 points determine a degree 3 polynomial function and 5 points determine a degree 4 polynomial function.
As you drag the points indicated in the graphs, the function and graph are updated. As you drag points in the Quartic applet, you see that degree 4 polynomial graphs can have a variety of shapes. Cubic degree 3 Quartic degree 4.
Monomials of the form x n have graphs that can be sketched easily even when n is larger than 2. To begin with, all such graphs go through the origin 0, 0 and the point 1, 1. When n is even, the graph of x n is symmetric with respect to the y-axis and contains the point -1, 1. When n is odd, the graph of x n is symmetric with respect to the origin and contains the point -1,
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