91Ó°ÊÓ

Define a quadratic function \(y=f(x)\) that satisfies the given conditions. Axis of symmetry \(x=4,\) maximum value \(6,\) passes through (1,3)

Write a polynomial \(f(x)\) that meets the given conditions. Answers may vary. (See Example 10 ) Degree 2 polynomial with zeros \(5 \sqrt{2}\) and \(-5 \sqrt{2}\).

Define a quadratic function \(y=f(x)\) that satisfies the given conditions. Axis of symmetry \(x=-2,\) minimum value \(5,\) passes through (2,13)

Determine if the statement is true or false. The function defined by \(g(x)=-3(x+4)(2 x-3)^{4}\) touches but does not cross the \(x\) -axis at \(\left(\frac{3}{2}, 0\right)\).

Find the value of \(b\) or \(c\) that gives the function the given minimum or maximum value. $$ f(x)=2 x^{2}+12 x+c ; \text { minimum value }-9 $$

Write a polynomial \(f(x)\) that meets the given conditions. Answers may vary. (See Example 10 ) Degree 3 polynomial with zeros \(-2,3 i,\) and \(-3 i\).

Determine if the statement is true or false. A third-degree polynomial has two turning points.

Find the value of \(b\) or \(c\) that gives the function the given minimum or maximum value. $$ f(x)=3 x^{2}+12 x+c ; \text { minimum value }-4 $$

Write a polynomial \(f(x)\) that meets the given conditions. Answers may vary. (See Example 10 ) Degree 3 polynomial with zeros \(4,2 i\), and \(-2 i\).

Write a polynomial \(f(x)\) that meets the given conditions. Answers may vary. (See Example 10 ) Degree 3 polynomial with integer coefficients and zeros of \(-\frac{2}{3}, \frac{1}{2},\) and 4