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How do you graph y equals x to the fourth plus 2x cubed plus x squared plus 8x minus 12 without a calculator?
(1) Find the x-intercepts (by setting y=0 and solving for x).
(2) Find the y-intercepts (by setting x=0 and solving for y).
(3) OPTIONAL: Check for symmetries. If a point (x,y) is on the graph, is the point (-x,y) also on the graph (that is symmetry about the y-axis)? Is the point (-x,-y) on the graph (that is symmetry about the origin)? There are many kinds of symmetries.
(4) Check for vertical asymptotes--normally you would set the denominator ONLY equal to zero and solve for x, but this equation does not have any fractions, so don't worry about this step.
(5) Check for horizontal asymptotes--what is the limit of the equation as x approaches infinity? Negative infinity? (In this example the limit will not exist; the graph will go toward infinity as x gets bigger.)
(6) Use the first derivative test to find the maximums and minimums, as well as to determine the intervals where the graph increases and decreases.
(7) Use the second derivative test or concavity test to find points of inflection and/or concavity.
(8) Wherever the behavior of the graph is still unclear, simply plug in some test values for x and see what you get for corresonding y values.
What else can I help you with?
Parabola y equals one-fourth x squared?
Yes.
What is one fourth of 45000.00?
11250.00 without the aid of a calculator.
How do you enter ten to the fourth power on a calculator?
To enter ten to the fourth power on a calculator, you can typically use the exponentiation function. First, input the number 10, then press the exponent key (often labeled as "^" or "x^y"), followed by entering the number 4. Finally, press the equals key to obtain the result, which is 10,000.
What is the answer to 3x squared squared 5x to the fourth?
(3x2)2 (5x)4 = 9x4625x4 = 5625x8
What is the numerical answer for 3 to the fourth power plus 5 squared?
106
Parabola y equals one-fourth x squared?
Yes.
What is one fourth of 45000.00?
11250.00 without the aid of a calculator.
How does one half squared equal one fourth?
One half squared equals one fourth because when you multiply one half by one half you get one fourth. This is the equivalent of saying that half of one half is one fourth.
A squared over A to the fourth?
One over A squared or A to the negative 2.
What is b squared times b squared?
b to the fourth power
What to the fourth power equals 48?
± 2.632148 to the fourth power equals 48.
How do you enter ten to the fourth power on a calculator?
To enter ten to the fourth power on a calculator, you can typically use the exponentiation function. First, input the number 10, then press the exponent key (often labeled as "^" or "x^y"), followed by entering the number 4. Finally, press the equals key to obtain the result, which is 10,000.
What is the answer to 3x squared squared 5x to the fourth?
(3x2)2 (5x)4 = 9x4625x4 = 5625x8
What is one fourth squared as a fraction?
It is 1/16.
What is The greatest common factor of 84 and 144?
The GCF of 84 and 144 is 12. You must do the prime factorization of each number. The prime factorization of 144 is 2 to the fourth power times 3 squared. The prime factorization of 84 is 2 squared times 7 times 3. You take the least of each common factor which would be 2 squared and 3. Two squared equals 4 and 4 times 3 equals 12, so the GCF is 12.
Which is greater 2 to the power of 4 or 8 to the power of 2?
"2 to the power of 4" is written "two to the fourth power", and "8 to the power of 2" is known as "eight squared". And, eight squared is greater than two to the fourth power. Eight squared is 64, and two to the fourth power is 16.
What are four squared divided by two to the fourth power?
1
