The correct option is,
⇒ The graph crosses the x-axis at x = -2 and x = 1 and touches the x-axis at x = 0.
A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given function is,
f(x) = x⁴ + x³ - 2x²
Now, We can simplify as;
f(x) = x⁴ + x³ - 2x²
= x²(x² + x - 2)
= x²(x² + 2x - x - 2)
= x²[x(x + 2) - 1(x + 2)]
= x²(x + 2)(x - 1)
So the factored form of the polynomial function is,
f(x) = x²(x + 2)(x - 1)
For x - intercepts,
F(x) = x²(x + 2)(x - 1) = 0
x = -2, 1
This function has even multiplicity = 2 at x = 0.
Therefore, graph of the function will touch the x-axis at x = 0
And at other roots x = -2, 1 has odd multiplicity = 1, so the graph will cross the x-axis.
Thus, Option (3) will be the correct option.
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Answer: C. The graph crosses the x-axis at x=-2 and x=1 & touches the x-axis at x=0
Step-by-step explanation:
You can tell this by factoring the equation to get the zeros. To start, pull out the greatest common factor.
f(x) = x^4 + x^3 - 2x^2
Since each term has at least x^2, we can factor it out.
f(x) = x^2(x^2 + x - 2)
Now we can factor the inside by looking for factors of the constant, which is 2, that add up to the coefficient of x. 2 and -1 both add up to 1 and multiply to -2. So, we place these two numbers in parenthesis with an x.
f(x) = x^2(x + 2)(x - 1)
Now we can also separate the x^2 into 2 x's.
f(x) = (x)(x)(x + 2)(x - 1)
To find the zeros, we need to set them all equal to 0
x = 0
x = 0
x + 2 = 0
x = -2
x - 1 = 0
x = 1
Since there are two 0's, we know the graph just touches there. Since there are 1 of the other two numbers, we know that it crosses there.
Answer:
the answer is 'undefined'
Step-by-step explanation:
Cot is defines as (cos x)/(sin x)
So we can rewrite our expression as...
(cos 180°)/(sin 180°) + (cos 180°)/(sin 180°)
or
2(cos 180°)/(sin 180°)
Cos 180° = 1, sin 180° = 0 (you get these from the unit circle)
so we have
2(1/0) = 2/0, which is undefined, because we don't divide by zero
Answer: 223 - 119 = 104
Step-by-step explanation:
For subtracting 223-119,we will write this as
H T O
2 2 3
- 1 1 9
Noe start from the right we can't subtract 9 from 3 so combine tens and ones places so that 23-19=04(should remember to place 0 before 4), after that we can simply solve the hundred to get the final answer.
H T O
2 2 3
- 1 1 9
1 0 4
So 104 is the answer.
Answer:
X=2
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
120(2x−2)=240
(120)(2x)+(120)(−2)=240(Distribute)
240x+−240=240
240x−240=240
Step 2: Add 240 to both sides.
240x−240+240=240+240
240x=480
Step 3: Divide both sides by 240.
240x/240=480/240
x=2
A. y=-2x^2-8x
B. y=2(x+6)(x-2)
C. y=x^2-8x+16
D. y=2(x+4)^2-2
Use the equations to complete the following statements.
Equation (A,B,C, or D) reveals its extreme value without needing to be altered. The extreme value of this equation has a (minimum or maximum) at the point (-4,-3,0 or 2 , -32,-8,8, or -2 ).
From each of the given equations, the option which gives a squared expression for the variable with x ; hence does not need any further mathematical calculation in other to determine it's extremes is the expression y = 2(x+4)² - 2 ; option (D) with minimum at the points (-4, - 2)
The extreme vlaue of an expression has a minimum at ;
Obtain the value of x when (x + 4) = 0:
x = - 4
Substitute -4into the equation :
y = 2(-4 + 4)² - 2
2(0) - 2 = - 2
Therefore, the equation has its extremesat (-4,-2)
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Answer:
Step-by-step explanation: