The required inequality is y < (x + 2) + 3
How to find the inequality represented by the graph?
To find the inequality representing the graph, we need to find the equation of the curve.
We see that the curve is a parabola. So representing the parabola in vertex form with vertex (h, k) , we have
y = a(x - h) + k where
- h = x - intercept of vertex and
- k = y - intercept of vertex
Now, from the graph, we see that
- the x - intercept of the vertex, h = -2 and
- the x - intercept of the vertex, k = 3
So, substituting these into the equation, we have
y = a(x - h) + k
y = a(x - (-2)) + 3
y = a(x + 2) + 3
Also, we see that the graphintercepts the y- axis at (0, 5)
So, substituting these into the equation, we have
y = a(x + 2) + 3
5 = a(0 + 2) + 3
5 = a(2) + 3
5 = 2a + 3
5 - 3 = 2a
2a = 2
a = 2/2
a = 1
So, the equation of the parabola is y = (x + 2) + 3
From the graph, we see that the region shaded is the region below the parabola y = (x + 2) + 3. Also, the curve is not dashed so, it is not included in the region, thus we use the < sign.
So, the required inequality is y < (x + 2) + 3
Learn more about inequality here:
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