Solve 3x^2-12=-12 by graphing the related function.
To solve the equation 3x^2 - 12 = -12 by graphing, we need to plot the graph of the related function y = 3x^2 - 12 and find the x-values where y = -12.
To graph the function y = 3x^2 - 12, we can start by creating a table of values. We choose some x-values, calculate the corresponding y-values using the function, and plot the points on a graph.
Let's choose some x-values: x = -2, -1, 0, 1, 2, 3
Now, calculate the corresponding y-values using the function y = 3x^2 - 12:
For x = -2:
y = 3*(-2)^2 - 12 = 12 - 12 = 0
For x = -1:
y = 3*(-1)^2 - 12 = 3 - 12 = -9
For x = 0:
y = 3*(0)^2 - 12 = 0 - 12 = -12
For x = 1:
y = 3*(1)^2 - 12 = 3 - 12 = -9
For x = 2:
y = 3*(2)^2 - 12 = 12 - 12 = 0
For x = 3:
y = 3*(3)^2 - 12 = 27 - 12 = 15
Plotting these points on a graph, we get:
(3,15)
(2,0) (4,12)
(1,-9)
(3,-9)
(-2,0)
(-4,12)
(-1,-9)
(-3,15)
(0,-12)
(-2,0)
From the graph, we can see that the line y = -12 intersects the curve at x = 0. Therefore, the solution to the equation 3x^2 - 12 = -12 is x = 0.
Note: In this case, the graph helps us identify the solution more clearly. However, graphing may not be the most efficient method for solving quadratic equations.