Have been given a table of values and to complete it using the equation, y = x^2 - 3x + 10.
(-1,14), (0,10), (1,8), (2,?), (3,10), (4,?) and (5,20).
You draw a graph, using 2cm=1 unit on x-axis and 2cm=2 units on y-axis.
Now my question is...how do you solve the simultaneous equations using the graph:
y = x^2 - 3x + 10.
y = x + 7.
Seriously want help here...and explain more clearly
(-1,14), (0,10), (1,8), (2,?), (3,10), (4,?) and (5,20)
the missing values should be like:
(-1,14), (0,10), (1,8), (2,8), (3,10), (4,14?) and (5,20)
Now if you put those same x value into the straight line you get:
(-1,6), (0,7), (1,8), (2,9), (3,10), (4,11), and (5,12)
Notice that (1,8) and (3,10) are in both tables.
so x=1, y=8 and x=3,y=10 are your solutions.
Your graph should look like this
http://www.wolframalpha.com/input/?i=y+%3D+x%5E2+-+3x+%2B+10+,++y+%3D+x+%2B+7
To solve the simultaneous equations using the graph, you can follow these steps:
1. Plot the two graphs on the same Cartesian plane. Use the given scale to determine the points on the graph. For example, if 2cm on the x-axis represents 1 unit, and 2cm on the y-axis represents 2 units, then each point will be scaled accordingly.
2. The two lines will intersect at the point(s) where the solutions to the simultaneous equations lie. In this case, the equations are y = x^2 - 3x + 10 and y = x + 7.
3. Locate the points of intersection. These points will have the same x and y values, satisfying both equations simultaneously.
4. To find the missing values in the table, refer to the x-coordinate of the points of intersection on the graph. The corresponding y-coordinate will give you the solution in the table.
For example, in the given table:
(-1, 14), (0, 10), (1, 8), (2, ?), (3, 10), (4, ?), and (5, 20)
Plotting these points on the graph according to the given scale:
- Plot (-1, 14) -> (-2cm, 14cm)
- Plot (0, 10) -> (0cm, 10cm)
- Plot (1, 8) -> (2cm, 8cm)
- Plot (3, 10) -> (6cm, 10cm)
- Plot (5, 20) -> (10cm, 20cm)
Now, draw the graphs of the two equations:
- The graph of y = x^2 - 3x + 10 will be a parabola opening upwards.
- The graph of y = x + 7 will be a straight line with positive slope.
Locate the points where the two graphs intersect. These will be the solutions to the simultaneous equations.
Next, identify the x-coordinate of the points of intersection and find the corresponding y-coordinate on the graph. Use this information to complete the missing values in the table.
For instance, on the graph, you will find that the lines intersect at x = 2 and x = 4. To find the missing values:
- For (2, ?), locate the point on the graph where x = 2, and read the corresponding y-coordinate. This will give you the missing value.
- For (4, ?), do the same process but locate x = 4 on the graph to determine the corresponding y-coordinate. This will give you the missing value.