Posted by Julian Martinez

1. Sec 3.4 p. 155 #21
 We first identify the type of form the function is in.
 A Quadratic Function can be written in several common forms:
 General Form f(x)= ax² + bx + c
 Standard Form f(x)= a(x-h)² + k
 Factored Form f(x)= a(x-r)(x-s)
 With this information in mind we can identify that the function is in General(also
known as expanded) form.
 Since the function is in general form.
 We first calculate the x-coordinate of the vertex with formula.
 ℎ =
−𝑏
2𝑎
 ℎ =
−(−6)
2(−1)
=
6
−2
h = - 3
 Then find the y-coordinate by plugging it back in to graphing function.
 f(x)= -(-3)² - 6(-3) + 3
f(x)= -9 + 18 + 3
f(x)=12
 Vertex(-3,12)
 Identifying the direction the parabola opens.
 The Vertex is the Highest or lowest point on the graph, depending on end behavior.
 If the slope is represented positive; the Parabola opens up ,and the vertex is the
minimum
 If the slope is represented with a negative; Parabola opens down, and the vertex is the
maximum
 With this information the parabola is a maximum.
 -x² - 6x + 3
 This problem is fairly easy when you identify the function at hand.