Question 1120339: 4. Determine the quadratic function f whose graph is given.
The vertex is (3,-4) and the other given point is (1,4)
6. g(x) = 1/5 x -4, Determine the slope and y-intercept of the function., Use the slope and y-intercept to graph the linear function. Determine the average rate of change of the function. Determine whether the linear function is increasing, decreasing, or constant
9. Find the vertical, horizontal, and oblique asymptotes, if any, for the given rational function.
G(x) = x^4 – 1 / 3x^2 – 3x
7. Analyze the polynomial function f(x)= (x+3)^2 (x-6)^2
Determine the end behavior of the graph of the function.
Find the x- and y-intercepts of the graph of the function.
Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept.
Determine the maximum number of turning points on the graph of the function.
Use the above information to draw a complete graph of the function.
sorry its so many, I worked the problems some came up wrong, I need to see the steps to pls and thank you
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Post each question separately. Show the work you have done. Describe what it is that is causing you difficulty.
I'll help with the first one here.
4. You are given two points on a graph and asked for the quadratic function. In order to uniquely determine a quadratic, you need three points. That is because, in general, to uniquely determine a polynomial function of degree  you need  points.
Fortunately, one of the given points is identified as the vertex of the parabola graph. So, by symmetry, a third point can be determined. The vertex is at (3,-4) and the other point, (1, 4) is 2 units distant in the  -axis. Hence there is another point on the parabola 2 units on the other side of the vertex with a function value of 4, namely the point (5, 4).
We begin with the general quadratic function:
\ =\ ax^2\ +\ bx\ +\ c)
Since the point (1, 4) is on the graph, the following must be true about the desired function:
\ =\ 4)
So:
^2\ +\ b(1)\ +\ c\ =\ 4)
which simplifies to
Similarly, since we know that (3,-4) and (5,4) are on the graph:
and
We now have a 3X3 linear system. All you need to do is solve the 3X3 system to obtain the necessary coefficients for your function. Hint: Use the MDETERM function in Excel (or Numbers if you are on a Mac) to find the values of the four determinants necessary to solve the system using Cramer's Rule. There are also several online linear system solvers available.
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John
My calculator said it, I believe it, that settles it
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