Graph the equation.
5xx + y = -9
To graph the equation 5x^2 + y = -9, we need to rearrange it in the form y = f(x).
First, subtract -9 from both sides to isolate the term involving y:
5x^2 + y + 9 = 0
Next, rearrange the terms:
y = -5x^2 - 9
This equation represents a downward-opening parabola because the coefficient of x^2 is negative.
To graph the equation, we can start by creating a table of values for x and y.
Let's choose some x-values and calculate the corresponding y-values:
When x = -2, y = -5(-2)^2 - 9 = -5(4) - 9 = -20 - 9 = -29
When x = -1, y = -5(-1)^2 - 9 = -5(1) - 9 = -5 - 9 = -14
When x = 0, y = -5(0)^2 - 9 = -5(0) - 9 = 0 - 9 = -9
When x = 1, y = -5(1)^2 - 9 = -5(1) - 9 = -5 - 9 = -14
When x = 2, y = -5(2)^2 - 9 = -5(4) - 9 = -20 - 9 = -29
We can plot these points on a graph and connect them to create the graph of the equation.
The graph of the equation 5x^2 + y = -9 is a downward-opening parabola that passes through the points (-2,-29), (-1,-14), (0,-9), (1,-14), and (2,-29).