The graph of a function f is shown below. Find one value of x for which f(x) = -4 and find f (2).

Solution:

The above graph represents a general from of the quadratic equation of the form y = ax² + bx + c where a ≠ 0

The coordinate of the vertex of the graph shown is (0, -4).

The x-coordinate of the vertex is given by -a/2b.

Therefore

x = 0 = -b/2a

b = 0

Hence the general form of the equation of the parabola is modified to:

y = ax² + c

At the vertex y = -4, therefore

y = -4 = a(0)² + c

-4 = c

Therefore the equation becomes:

y = ax² - 4

To find the value of a we look at another point on the parabola i.e. (-4,4)

4 = a(-4)² - 4

8 = 16a

a = 1/2 = 0.5

Therefore the equation of the parabola is:

y = (1/2)x² - 4

Therefore

f(2) = (1/2)(2)² - 4

= -2

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The graph of a function f is shown below. Find one value of x for which f(x) = -4 and find f (2).

Summary:

One value of x for which f(x) = -4 is x =0. f (2) = -2