5.f(x) = x^4 - 16x^2
7.x^4 + 5x^3 - 84x^2 = 0
could you help me with the following,I don't understand.
Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.
1.f(x) = (x + 1)(x - 3)(x - 1)^2
5.f(x) = x4 - 16x2
7.x4 + 5x3 - 84x2 = 0
2 answers
4th degree functions can have a maximum of 4 x-intercepts (in general a nth degree function can have at most n x-intercepts)
They tend to look like a W
for 1.
the factors are (x+1)(x-3)(x-1)^2
so there are x-intercepts at -1 and 3.
The factor (x-1)^2 or (x-1)(x-1) tells us that the graph "touches" the x-axis at 1
Whenever you have a squared factor such as (x-a)^2 the curve would touch at a
For 7. factor it this way
x^2(x^2 + 5x - 84)
=x^2(x+12)(x-7)
the graph would touch at the origin, and cut the x-axis at -12 and 7
let me know what you got for #5
They tend to look like a W
for 1.
the factors are (x+1)(x-3)(x-1)^2
so there are x-intercepts at -1 and 3.
The factor (x-1)^2 or (x-1)(x-1) tells us that the graph "touches" the x-axis at 1
Whenever you have a squared factor such as (x-a)^2 the curve would touch at a
For 7. factor it this way
x^2(x^2 + 5x - 84)
=x^2(x+12)(x-7)
the graph would touch at the origin, and cut the x-axis at -12 and 7
let me know what you got for #5
1 answer