How do you graph the parabola y equals x squared plus 4x plus 3?

Answer 1

You need graph paper upon which you draw 2 lines at right angles. These are called the "axes" (singular is axis). The x axis should be near the centre of the graph paper and running horizontally; the y axis should be near the centre of the graph paper and running vertically.

Now you have to put a scale along each axis; the x axis should run left to right from negative numbers to positive numbers;the y axis should run from negative numbers at the bottom part and positive numbers above the "origin".

The origin is where the axes cross where the two scales read zero. That is the point (0,0); x numbers written first.

Then you have to compile a table of "values" of y for lots of separate values of x

Example sfor y = x^2 + 4x + 3 (where the sign ^ means "to the power of"

If x = 0, y = 3;

If x = 1, y = 1^2 + (4 x 1) + 3 = 1 + 4 + 3 = 8

If x = 2, y = 2^2 + (4 x 2) + 3 = 4 + 8 + 3 = 15

So we have found the x and y values for 3 points so far; they are (0,3); (1,8) and (2,15) and these can now be "plotted" onto the graph paper, remembering that the x value is the left hand one of each pair.

To plot the point (3, 24) you would go +3 on the x axis and "up" as far5 as 24 on the y axis.

As you keep on calculating more values of x for values of y you will be able to plot many more points; the more you plot the more you will be able to see the shape of the curve which represents y = x^2 + 4x + 3

or

y = x2 + 4x + 3

Let x = 0, then (0, 3) is the y-intercept point (plot it).

Let y = 0, then (x + 3)(x +1) = 0 so that (-3, 0) and (-1, 0) are the x-intercepts points (plot them).

Since -2 is midway -3 and -1, x = -2 is the equation of the axis of symmetry. So you can plot (-4, 3) as it is the symmetric point of (0,3).

Since the vertex lies on the axis of symmetry, -2 is the x-coordinate of the vertex, and its y-coordinate it will be -1, as you replace -2 with x into the equation. So go and plot (-2, -1), the vertex.

Now draw a smooth curve that passes through the points that you've just plotted. And you're done, that is your parabola.