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Below are suppose the be the questions:
a. factor the equation
<span>b. graph the parabola </span>
<span>c. identify the vertex minimum or maximum of the parabola </span>
<span>d. solve the equation using the quadratic formula
</span>
below are the answers:
Vertex form is most helpful for all of these tasks.
<span>Let </span>
<span>.. f(x) = a(x -h) +k ... the function written in vertex form. </span>
<span>a) Factor: </span>
<span>.. (x -h +√(-k/a)) * (x -h -√(-k/a)) </span>
<span>b) Graph: </span>
<span>.. It is a graph of y=x^2 with the vertex translated to (h, k) and vertically stretched by a factor of "a". </span>
<span>c) Vertex and Extreme: </span>
<span>.. The vertex is (h, k). It is a maximum if "a" is negative; a minimum otherwise. </span>
<span>d) Solutions: </span>
<span>.. The quadratic formula is based on the notion of completing the square. In vertex form, the square is already completed, so the roots are </span>
<span>.. x = h ± √(-k/a)</span>
For each subset it can either contain or not contain an element. For each element, there are 2 possibilities. Multiplying these together we get 27 or 128 subsets. For generalisation the total number of subsets of a set containing n elements is 2 to the power n.
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