Question 1443: y = -3x(squared)
I need to find out the vertex, roots, if opens upward or downward, different points in order to graph parabola, and using the quadratic equation for something.
Answer by AnlytcPhil(1806)   (Show Source):
You can put this solution on YOUR website! y = -3x(squared) I need to find out the vertex, roots, if opens upward or downward, different points in order to graph parabola, and using the quadratic equation for something.
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Make a table of values. choose x = -2, -1, 0, 1 and 3
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Substitute -2 for x in y = -3x²
y = -3x²
y = -3(-2)²
y = -3(4)
y = -12
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So one point is (-2, -12). Plot that point.
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Substitute -1 for x in y = -3x²
y = -3x²
y = -3(-1)²
y = -3(1)
y = -3
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So another point is (-1, -3). Plot that point.
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Substitute 0 for x in y = -3x²
y = -3x²
y = -3(0)²
y = -3(0)
y = 0
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So another point is (0, 0). Plot that point.
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Substitute 1 for x in y = -3x²
y = -3x²
y = -3(1)²
y = -3(1)
y = -3
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So another point is (1, -3). Plot that point.
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Substitute 2 for x in y = -3x²
y = -3x²
y = -3(2)²
y = -3(4)
y = -12
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So another point is (2, -12). Plot that point.
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Now when you connect these points you get
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The vertex is the turning point (at the top. It is (0,0)
Its root(s) is(are) found by setting y=0 ands solving for x.
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y = -3x²
0 = -3x²
3x² = 0
x² = 0
x = 0
So the only root is 0.
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You can see that it opens downward, which will always be the case
if the coefficient of x² is negative.
I don't understand "using the quadratic equation for something."
Edwin
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