91Ó°ÊÓ

The graph of \(f(x)=3(x-2)^{2}-6\) is a parabola that opens _____ with its vertex at (_____,_____), and \(f(2)=\) _____ is the (minimum/maximum) _____ value of \(f\).

Graphing Quadratic Functions A quadratic function \(f\) is given. (a) Express \(f\) in standard form. (b) Find the vertex and \(x\) and \(y\) -intercepts of \(f .\) (c) Sketch a graph of \(f .\) (d) Find the domain and range of \(f\). $$f(x)=x^{2}+8 x$$

A polynomial function \(P\) and its graph are given. (a) List all possible rational zeros of \(P\) given by the Rational Zeros Theorem. (b) From the graph, determine which of the possible rational zeros actually turn out to be zeros. $$P(x)=4 x^{4}-x^{3}-4 x+1$$ (GRAPH CANNOT COPY)

Graphing Factored Polynomials Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$P(x)=x^{3}(x+2)(x-3)^{2}$$

Graphing Polynomials Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. $$P(x)=x^{3}+3 x^{2}-4 x-12$$

Finding Quadratic Functions Find a function \(f\) whose graph is a parabola with the given vertex and that passes through the given point. $$\text { Vertex }(-1,5) ; \quad \text { point }(-3,-7)$$

Maximum of a Fourth-Degree Polynomial Find the maximum value of the function $$f(x)=3+4 x^{2}-x^{4}$$

Graph the polynomial in the given viewing rectangle. Find the coordinates of all local extrema. State each answer rounded to two decimal places. State the domain and range. $$y=x^{4}+4 x^{3}, \quad[-5,5] \text { by }[-30,30]$$

A polynomial \(P\) is given. (a) Find all the real zeros of \(P .\) (b) Sketch a graph of \(P\).0 x+9. $$P(x)=x^{5}-x^{4}-5 x^{3}+x^{2}+8 x+4$$