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Question 115117: Can someone please help? I am having problems with this question and I need to turn in my homework on Saturday. Please help!!!!!!!
Consider the function f(x)=x^2+6x-2.
a) Find h, the x-coordinate of the vertex of this parabola.
b)Substitute the two whole number values immediately to the left and the right of h into the function to find the corresponding y. Fill in the table below. make sure your x values are in increasing order in your table.
x y
___ ___
___ ___
h= ___ ___
___ ___
___ ___
c) Use MS Excel to graph the function by plotting the points found in the table in part b.
Please, if anyone can help I will greatly appreciate it, I am totally confused with this one.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Since your deadline is Saturday, I can help a little, but you may need to post your problem
again to get additional help from other tutors.
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You can tell by the fact that the x^2 term is positive that the graph of this function is
a parabola that, as you move from left to right, falls to a minimum and then rises again ... in
other words it models the shape of a cup that is upright.
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The vertex of this parabola is the lowest point of the curve. h is the value of x where this
curve is at the lowest point.
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The quadratic formula applies to equations of the form ax^2 + bx + c = 0. By comparing
this form to your function of x^2 + 6x - 2 you will see that a = 1, b = +6, and c = -2.
The value of x at the vertex is given by -b/(2a). Substituting the values of "b" and "a"
that we found in by comparing with the quadratic form results in:
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x = -(+6)/(2*1) = -6/2 = -3
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This means that the value of h is -3.
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Now that you know this you can start to find f(x) by evaluating x^2 + 6x -2 at various
values of x on both sides of x = -3.
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For example, you can evaluate x^2 + 6x - 2 for x = -5, x = -4, x = -3, x = -2, and x = -1.
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When x = -5, then you will find that x^2 + 6x - 2 = y = -7
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When x = -4, then you will find that x^2 + 6x - 2 = y = -10
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When x = -3, then you will find that x^2 + 6x - 2 = y = -11
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When x = -2, then you will find that x^2 + 6x - 2 = y = -10
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When x = -1, then you will find that x^2 + 6x - 2 = y = -7
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If you plot these points, you should get an idea of the shape of the graph of y = x^2 + 6x - 2
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Here is the graph that you should get:
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Hope this information helps you to get started on this problem.
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