The line is intercepting on the x axis at (-2,0) (1,0) and (5,0) and a y intercept of (0,-4) you have to draw the graph first
So how do you find the equation The answer is suppose to be -2/5 (x+2)(x-1)(x-5)
So how do find that answer please explain don't understand how to find it! Please help thanks!
So how do you find the equation The answer is suppose to be -2/5 (x+2)(x-1)(x-5)
So how do find that answer please explain don't understand how to find it! Please help thanks!
-
1st step write down the intercepts) (-2,0) (1,0) and (5,0) if these are the x intercepts you just make the signs opposite and put an x in front of it like this (x+2)(x-1)(x-5) the spots the parabola crosses the horizontal line will always be in your equation of a parabola because to find the x intercepts you make y =0 and just focus on one set of brackets like this 0=(x+2) x = -2 meaning when y =0 the line crosses at negative 2. (if it crosses at 0 just put an x outside the brackets, but this one doesn't)
If one set of brackets is squared it means it bounces off this spot eg (x-7)^2, bounces off 7 if you have only one set of brackets and it's cubed just rearrange equation so x is on it's own and that's your x intercept like (x - 2)^3=0, x^3 -8=0 , x^3 = 8 x=2 and if the equation has no brackets, but loads of x's you'll need to factor it.None of this stuff applies to your cubic
2nd step find how much the cubic is dilated by if at all, this is shown by the number in front of the brackets) ok so basically to find the y intercept all the x's have to equal 0 and simplify all the leftover numbers, but right now (0-5)(0+2)(0-1) all this multiplied together does not equal -4 (which we know our y intercept is).So all we have to do is make it = -4 like this. A (0-5)(0+2)(0-1)= -4 A10=-4
A=-2/5
so our cubic's equation should be -2/5 (x+2)(x-1)(x-5)
If one set of brackets is squared it means it bounces off this spot eg (x-7)^2, bounces off 7 if you have only one set of brackets and it's cubed just rearrange equation so x is on it's own and that's your x intercept like (x - 2)^3=0, x^3 -8=0 , x^3 = 8 x=2 and if the equation has no brackets, but loads of x's you'll need to factor it.None of this stuff applies to your cubic
2nd step find how much the cubic is dilated by if at all, this is shown by the number in front of the brackets) ok so basically to find the y intercept all the x's have to equal 0 and simplify all the leftover numbers, but right now (0-5)(0+2)(0-1) all this multiplied together does not equal -4 (which we know our y intercept is).So all we have to do is make it = -4 like this. A (0-5)(0+2)(0-1)= -4 A10=-4
A=-2/5
so our cubic's equation should be -2/5 (x+2)(x-1)(x-5)
-
Knowing the intercepts you can easily get the last part of the equation: y=(x+2)(x-1)(x-5)
But if you try finding the y-intercept of this graph it will come (0,10).
Therefore there must have been a transformation done to the graph. To find this transformation we need to do:
x * 10 = -4
Therefore x=-4/10
x=-2/5
The equation is y= -2/5(x+2)(x-1)(x-5)
EDIT---------------
The y-intercept -10 that I showed you was not correct. It's just used to find by how much the graph has changed. Have you done transformations yet?
But if you try finding the y-intercept of this graph it will come (0,10).
Therefore there must have been a transformation done to the graph. To find this transformation we need to do:
x * 10 = -4
Therefore x=-4/10
x=-2/5
The equation is y= -2/5(x+2)(x-1)(x-5)
EDIT---------------
The y-intercept -10 that I showed you was not correct. It's just used to find by how much the graph has changed. Have you done transformations yet?