Write the quadratic function 5x2 - 40x + 60 in its vertex form by completing the square. Then
2 answers:
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Answer:
- 5(x -4)² -20
- turning point = (4, -20)
Step-by-step explanation:
It can work well to factor the leading coefficient from the x-terms.
5(x² -8x) +60
Now, add the square of half the x-coefficient inside parentheses, and subtract the same amount outside parentheses.
5(x² -8x +16) +60 -(5)(16)
5(x -4)² -20 . . . . write as a square, simplify the added constant
The vertex form is ...
5(x -4)² -20
It shows you the vertex is (4, -20). This is the turning point.
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Vertex form is a(x -h)² +k, where (h, k) is the vertex.
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The points on the graph are:
- Midline point = (0,-5)
- Maximum point = (0.65,-2)
The equation of the function is given as:
See attachment for the graph of the function f(x)
<h3>(b) The midline point</h3>This is the point that is on the line that passes through the midsegment of the function.
From the graph, a point on the midline is (0,-5)
<h3>(c) The maximum point</h3>This is the point that is on the vertex of the function.
From the graph, a point on the midline is (5pi/24,-2)
This can be rewritten as: (0.65,-2)
Read more about trigonometry graphs at:
