3.(08.07 HC) An expression is shown below:
f(x) = -16x2 + 22x + 3
Part A: What are the x-Intercepts of the graph of the f(x)? Show your work. (2 polnts)
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
(10 points)

For a general equation:

y = f(x) =  a*x^2 + b*x + c

The x-intercepts are given by:

And the vertex is the point (h, k) such that:

h = -b/2*a

k = f(h)

Part A)

We have the function f(x) = -16*x^2 + 22*x + 3

The x-intercepts are then:

The two intercepts are:

x = (-22 - 26)/(-32) = 1.5

x = (-22 + 26)/(-32) = -0.125

Part B:

The vertex is (h, k), such that:

h = -22/(2*(-16)) = -22/-32 = 0.6875

k = f(0.6875) = -16*(0.6875)^2 + 22*0.6875 + 3 = 10.6525

Then the vertex is: ( 0.6875, 10.6525)

If the leading coefficient is positive, then the vertex is a minimum

If the leading coefficient is negative, then the vertex is a maximum.

In this case the leading coefficient is -16, then we can conclude that the vertex is a maximum.

Part C:

To graph the function, we can graph the points that we already know (the vertex and the two x-intercepts) and connect them with a curve.

You could also add another few points so you have a guide to draw the curve, for example the point:

y = f(0) = -16*0^2 + 22*0 + 3

    f(0) = 3

(0, 3)

439400

step-by-step explanation:

130^2 = 16900

16900*26 = 439400