x^4-10x^2+9 graphed and solved

Question

we are graphing polynomail functions using the end behavior, the zeros of a function and other helpful points.

Answer 1

This factorises into (x^2-9)(x^2-1)=(x-3)(x+3)(x-1)(x+1). For graphing purposes we can see there are four zeroes at x=-3, -1, 1 and 3. The curve must pass through these points (-3,0), (-1,0), (1,0) and (3,0) on the x-axis. When x is large and positive the expression (which we can y) is also large and positive, and when large and negative, y is large and positive. So the graph comes in from the left (negative side of x, above the x-axis) cuts the axis at -3, turns round like a Big Dipper ride and cuts it again at -1, turns round again and cuts it at 1 and again at 3 and continues on the right above the x-axis. The curve cuts the y-axis when x=0 at y=9, so between x=-1 and 1 it cuts the y-axis at y=9. The curve looks like a W.

Answer 2

Given x^4-10x^2+9
x^4-9x^2-x^2+9
x^2(x^2-9)-1(x^2-9)
(x^2-1)(x^2-9)
(x^2-1)(x^2-3^2)
(x-1)(x+1)(x-3)(x+3)
x=1,-1 or x=-3,

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Algebra Functions