The system of inequalities represented on the graph is:
What is a linear function?
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The linear function in this problem has y-intercept of b = 3, and also goes through the point (1,5), hence the slope is of 2. The line is dashed, hence it is not included in the solution, hence only the part greater than the line is, hence:
y > 2x + 3
What is the equation of a parabola given it’s vertex?
The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this graph, the vertex of the parabola is of (-1,-4), hence h = -1, k = -4, and the equation is:
y = a(x + 1)² - 4
When x = 0, y = -3, hence the leading coefficient is found as follows:
-3 = a - 4
a = 1.
Hence:
y = (x + 1)² - 4.
And the inequality is:
y > (x + 1)² - 4.
More can be learned about a system of inequalities at https://brainly.com/question/3656398
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