Question

How do I graph: Y=2x^2+16x+30? please show how to solve. ty

Answer 1

Answer:

  graph several points and draw a curve through them

Step-by-step explanation:

First of all, I would remove the common factor of 2 from the coefficients. This makes it easier to see how the equation might be factored.

  y = 2(x^2 +8x +15)

The constant 15 has factors 1, 3, 5, 15. The two that add up to 8 are 3 and 5, so this can be further factored as ...

  y = 2(x +3)(x +5)

This tells you the x-intercepts (where y=0) are x=-3 and x=-5.

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The line of symmetry is halfway between, at x = -4. The vertex value is the value of y at that point:

  y = 2(-4+3)(-4+5) = 2(-1)(1) = -2

So, the minimum is (-4, -2). The graph crosses the x-axs at x=-5 and -3. The overall factor of 2 tells you this is expanded vertically by a factor of 2, so the curve goes up by double the square of the distance from the axis of symmetry: points (-2, 6), (-1, 16), and their reflections across the line of symmetry, (-6, 6), (-7, 16) are all on the curve.

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So, the graph will start with the points you know:

  (-4, -2), (-5, 0), (-3, 0), (-6, 6), (-2, 6), (-7, 16), (-1, 16)

Then you draw a smooth curve through them.

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Personally, I like to use a graphing calculator to draw the graph.