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The x-coordinate of the vertex of the parabola
f(x)=ax^2+bx+c
is given by the formula... |
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What is the leading term of..
f(x)=(3x^4+3x^2)/8
is... |
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| The Leading Term and the Leading Coefficient are... |
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Definition
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What is the leading coefficient of..
f(x)=(3x^4+3x^2)/8
is... |
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| To find the y-intercept of a function you must... |
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Definition
| Make x equal to zero and solve |
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What is the y-intercept of...
x^3+3x^2+6x+12 |
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| What shape does x^3 make? |
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Definition
| A S shape rotated to the right, it essentially looks like a squiggle line. |
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| For the leading term if the exponent is odd and the coefficient is negative... |
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Definition
| The graph will rise to the left and fall to the right |
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When finding the zeroes of a problem in the form...
ax^2(x+b)
You Must... |
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Definition
Must set
ax^2=0
And Solve
Then Set (x+b)=0
and Solve |
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| How do you find the multiplicity of a zero and its end behavior? |
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Definition
1.) Refer to the original exponent in the problem you solved to find the zero.
2.) The degree of that exponent is the multiplicity.
3.) If the multiplicity is even it touches but does not cross the x-axis.
4.)If the multiplicity is odd it crosses the x-axis. |
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How do you find the intervals above and below the x-axis...
ax^2(x+b) |
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Definition
Above the X-Axis:
(Negative Infinity,b of the opposite sign)
Below the X-axis:
(b of the opposite sign, 0) (0,Infinity) |
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If f satisfies the condition
f(x)=f(-x) |
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Definition
| Then the Graph Is Symmetrical About the Y-axis |
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If f satisfies the condition
f(-x)=-f(x) |
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| Then it is Symmetrical About the Origin |
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Definition
| Equals the Number of Turning Points |
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The n value of
ax^2(x+b)
is... |
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How do you find the intervals above and below the x-axis...
x(x+a)(x-a)(x+b) |
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Definition
Above the X-axis:
(-Infinity,-a)U(-b,0)U(a,infinity)
Order based on number size matters
Below the X-axis:
(-b,-a)U(0,a)
Order based on number size matters |
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Find The set of rational zeroes
for
ax^3+bx^2+cx-d
Where "a" and "d" are divisible |
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Definition
The three zeros are:
-d,-1/d, 1/(a/d) |
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| How to find the domain of a rational function |
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Definition
1.) Factor the denominator into two factors, set them to zero and solve for a and b.
2.) a is the lowest number and b is highest number
3.) Set it in this form:
(-infinity,a)U(a,b)U(b,infinity) |
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| Set the denominator of the rational function equal to zero, and solve to find the... |
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Definition
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How do you find the horizontal asymptote of a rational function in the form
f(x)=-ax+b/cx+d |
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Definition
1.)-a/c
2.)If the degree of the numerator is larger than the denominator, the graph has no horizontal asymptote. If the degree of the denominator is larger than the degree of the numerator, the x-axis is the horizontal asymptote. |
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