The graph for the given function is plotted. The graph of a function is represented by y = f(x).
How to graph a function?
- Consider the given function as y = f(x)
- Consider some values for x and find y-values
- Pair these x and y values as coordinates and plot them in the graph
- Connect all the points forming a curve (since it is a quadratic function)
Graphing the given function:
The given function is f(x) = x² + 4x - 1
Consider x values as {-5, -4, -3, -2, -1, 0, 1, 2}
Substituting these values in the function for finding y-values
When x = -5
y = f(-5) = (-5)² + 4(-5) -1 = 4
∴ (-5, 4)
When x = -4
y = f(-4) = (-4)² + 4(-4) -1 = -1
∴ (-4, -1)
When x = -3
y = f(-3) = (-3)² + 4(-3) -1 = -4
∴ (-3, -4)
When x = -2
y = f(-2) = (-2)² + 4(-2) -1 = -5
∴ (-2, -5)
When x = -1
y = f(-1) = (-1)² + 4(-1) -1 = -4
∴ (-1, -4)
When x = 0
y = f(0) = 0 + 4(0) -1 = -1
∴ (0, -1)
When x = 1
y = f(1) = 1² + 4(1) -1 = 4
∴ (1, 4)
When x = 2
y = f(2) = 2² +4(2) -1 = 11
∴ (2, 11)
Plotting these points in the graph and connecting them gives a curve (parabola).
Checking for the vertex:
f(x) = a(x - h)² + k
⇒ x² + 4x - 1
⇒ (x - (-2))² -5
So, the vertex is (h, k) = (-2, -5).
Learn more about the graph of a function here:
https://brainly.com/question/4025726
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