I need help on how to graph something.?

Question

how the h**l do you graph -2 x 2 + 8x - 5? and x 2 + 6x + 8? just so you know the first two x's in each problem are to the 2nd power. i'm so frustrated, someone help please.

Answer 1

The graph of y = ax^2 + bx + c is a parabola. If a is positive, the parabola opens upwards. If a is negative, the parabola opens downwards.

If you know how to complete the square for a quadratic function, you can find the lowest or highest point, which is called the vertex. The graph is symmetrical about the vertex.

- 2x^2 + 8x - 5 = y

Add 5 to get the absolute term isolated:

- 2x^2 + 8x = y + 5

Factor out the coefficient of x^2:

- 2(x^2 - 4x) = y + 5

Inside the bracket, add the square of half the coefficient of x, making a similar change on the other side:

- 2(x^2 - 4x + 2^2) = y + 5 - 2 * 2^2

The bracketed terms can be written (x - 2)^2:

- 2(x - 2)^2 = y - 3

(x - 2)^2 = - (1 / 2)(y - 3) ...(1)

The parabola (x - h)^2 = 4a(y - k) has vertex (h, k).

The vertex of (1) is therefore (2, 3).

That's the highest point on your graph.

To plot the rest, substitute other values of x, either in (1) or in the original equation, and find the orresponding value of y. Then join up the points you have plotted with a smooth curve. It will be symmetrical about the vertex.

You can still plot the graph without completing the square, but you will then find the vertex by experimentation.