I don't think my teacher gave me enough information to solve this problem. Can anyone solve it?

Question

f(x) is a polynomial. f(-1) = 4. f(1) = -3. f(4) = -6. Then the graph of f(x) must cross the x-axis at least how many times?

Do I need to know the degree of the polynomial?

Answer 1

You do have enough information, and you don't need to know the degree. The question isn't asking you how many times the graph does cross the x-axis, but rather the minimum number of times the graph must cross the x-axis based on the information you've been given. Since a polynomial is a continuous function, the graph has to cross the x-axis any time the sign of f(x) changes. In this case, the only sign change is between f(-1) = 4 and f(1) = -3, so there's only one guaranteed crossing of the x-axis with the information you have.

Answer 2

It has to cross the x axis at least once. It may cross more times, but at least once, because it has to get from +4 down to -1.

Answer 3

remember that the area of a loose-falling merchandise is given by using -16t^2 + (v_0)t + x_0, the place v_0 is the article's preliminary speed and x_0 is the article's preliminary place. enable's forget on the subject of the actuality that the bullet is vacationing horizontally for a minute, and merely communicate approximately its vertical place. Its preliminary vertical speed is 0, and its preliminary distance above the floor is 5. Plugging this into the equation, we get that an equation for its vertical action is x(t) = -16t^2 + 5. The bullet will strike the floor whilst x(t) = 0. enable's remedy: 0 = -16t^2 - 5 16t^2 = 5 t^2 = (5/sixteen) t = sqrt(5/sixteen). So the bullet will hit the floor after sqrt(5/sixteen) seconds. How far does the bullet holiday horizontally in this time? nicely, its horizontal speed is persevering with at 2600 feet/sec, so the horizontal distance it travels is sqrt(5/sixteen) * 2600 = approximately 1453. So i could say the respond is (d). (As an ingredient notice, the entire distance traveled is actual somewhat greater desirable than the horizontal distance--the bullet travels 1453 feet horizontally and 5 feet vertically, so the entire distance travelled is actual sqrt(5^2 + 1453^2), yet this nevertheless rounds to 1453--the vertical distance traveled seems to be insignificant.)

Answer 4

look to the variation of the function
once its 4 then its -3 then there is crossing after this it becomes
-6 (it was -3 and become -6)still in the minus so there is no crossing
get it?

Answer 5

once