Question 985391: How do I graph y=3x^2-2x-5
Found 3 solutions by josgarithmetic, Boreal, ikleyn:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! The zeros and the vertex, and understanding the coefficient of the leading term. Use Completing The Square to put into standard form, from which you can read the vertex coordinate values.
Also, you can take y=ax^2+bx+c, and do all the same and have a ready formula result to read the vertex coordinates more generally; and use for any general-form quadratic equation or function.
Answer by Boreal(15235)  (Show Source):
You can put this solution on YOUR website! Step 1, y-intercept. x=0, y=-5 from the equation. That is your first point.
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Step 2: find the vertex. The x-value is (-b/2a)=(2/6)=1/3.
the y-value is (1/3)-2/3-5=4 2/3. (1/3, -16/3) is the vertex. The x^2 coefficient is positive, so this is convex downward.
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Step 3: From the vertex to the y-intercept, you go left (1/3) unit and up 1/3 unit to (0,-5)
Step 4: Use symmetry, and go right 1/3 unit and up 1/3 unit. You have 3 points and can graph it, but these points are very close together. Therefore,
Step 5: Find zeros: This factors into (3x-5)(x+1)=0, so zeros are at x=(5/3) and -1. That gives 5 points.
Answer by ikleyn(52781)  (Show Source):
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