The function h(x) = x2 + 14x + 41 represents a parabola. Part A: Rewrite the function in vertex form by completing the square. S
how your work. (6 points) Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points) Part C: Determine the axis of symmetry for h(x). (2 points)
2 answers:
Part A:<span>
</span><span>
<span>
<span>
<span>
<span>
<span>
<span>
<span>
<span>
<span>
<span>
<span>
<span>
<span>
</span></span></span></span></span></span></span></span></span></span></span></span>
<span>
</span></span></span><span>
</span><span>
The first thing of completing the square is writing the
expression </span><span>
</span> as <span>
</span> which expands to <span>
</span>.<span>
We have the first two terms exactly alike with the function
we start with: </span><span>
</span>and <span>
</span> but we need to add/subtract from the last term, 49, to
obtain 41. <span>
So, the second step is to subtract -8 from the expression </span><span>
</span><span>
The function in finalizing the square form is
</span><span>
</span><span>
Part B:
The vertex is acquired by equating the expression in the
bracket from part A to zero
</span><span>
</span><span>
</span><span>
</span><span>
It means the curve has a turning point at x = -7
This vertex is a minimum since the function will make a
U-shape.
A quadratic function </span><span>
</span> can either make U-shape or ∩-shape depends on the
value of the constant <span>
</span> that goes with <span>
</span>. When <span>
</span> is (+), the curve is U-shape. When <span>
</span> (-), the curve is ∩-shape<span>
Part C:
The symmetry line of the curve will go through the vertex,
hence the symmetry line is </span><span>
</span><span>
<span>This function is shown in the diagram below</span></span>
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Cos(<span>θ) < 0, so we know it would be in Quadrant 2 or 3
then csc(</span>θ) = 257, but csc(θ) =
= 257
==> sin(<span>θ) =
it is positive, so now we can determine that is in Quadrant 2
sin(</span>θ) = opp./hyp both of opp and hyp are positive but adj suppose to negative because that way it leads the cos(<span>θ) < 0
</span>cos(<span>θ) = adj/hyp
</span>Pythereom to find the adj:
cosθ =
tanθ =
cos<span>θ = </span>
then csc(</span>θ) = 257, but csc(θ) =
==> sin(<span>θ) =
it is positive, so now we can determine that is in Quadrant 2
sin(</span>θ) = opp./hyp both of opp and hyp are positive but adj suppose to negative because that way it leads the cos(<span>θ) < 0
</span>cos(<span>θ) = adj/hyp
</span>Pythereom to find the adj:
cosθ =
tanθ =
cos<span>θ = </span>
The correct statement comparing the theoretical and experimental probabilities is given as follows:
.
A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.
The theoretical probability is taken before any experiment. Since the four sections are equal, the theoretical probability is:
T(H) = 1/4.
The experimental probability is taken considering previous experiments. Out of 100 tosses, 28 landed on H, hence:
E(H) = 28/100 = 7/25.
Hence the correct statement is:
.
More can be learned about probabilities at brainly.com/question/14398287
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