Graph the following equation and state the axes of symmetry 3x^2-3y=12x+9
3x^2-3y=12x+9
divide by 3 and re-arrange
y = x^2 - 4x - 3
complete the square ...
y = x^2 - 4x + 4 - 4 - 3
= (x - 2)^2 - 7
http://www.wolframalpha.com/input/?i=plot+y+%3D+(x+-+2)%5E2+-+7
axis of symmetry: x = 2
To graph the equation 3x^2 - 3y = 12x + 9, we can first rearrange it into the standard form of a quadratic equation:
3x^2 - 12x + 3y = 9
Now, isolate the variable y by moving the terms with y to the right side:
3y = -3x^2 + 12x + 9
Divide through by 3 to simplify:
y = (-1/3)x^2 + 4x + 3
Now we have the equation in the form y = ax^2 + bx + c, which represents a parabolic curve.
To graph this equation, we can create a table of values by selecting different x-values, plugging them into the equation, and calculating the corresponding y-values. Let's select a range of x-values, for example, from -5 to 5.
For x = -5:
y = (-1/3)(-5)^2 + 4(-5) + 3
y = (-1/3)(25) - 20 + 3
y = -25/3 - 60/3 + 9/3
y = -76/3
For x = -4:
y = (-1/3)(-4)^2 + 4(-4) + 3
y = (-1/3)(16) - 16 + 3
y = -16/3 - 48/3 + 9/3
y = -55/3
Performing similar calculations for other x-values within the range, we obtain the following table:
| x | y |
|-------|-------|
| -5 | -76/3 |
| -4 | -55/3 |
| -3 | -34/3 |
| -2 | -13/3 |
| -1 | 8/3 |
| 0 | 3 |
| 1 | 10/3 |
| 2 | 19/3 |
| 3 | 28 |
| 4 | 37/3 |
| 5 | 46/3 |
Now, plot the points from the table on a coordinate plane and connect them to form a smooth curve.
To find the axis of symmetry of the parabola, we can use the formula:
x = -b / (2a)
Looking at the equation y = (-1/3)x^2 + 4x + 3, we can identify a = -1/3 and b = 4. Plugging these values into the equation, we find:
x = -(4) / (2(-1/3))
x = -4 / (-2/3)
x = -4 * (-3/2)
x = 6
So, the axis of symmetry is x = 6.