Question Type 7: Sketching graphs of polynomials using technology Exercises

Sketch the graph of $f(x)=x^3-6x^2+9x+5$ using graphing software. Then determine the coordinates of its turning points.

Sketch $p(x)=-2x^3+x^2+3x-1$ using technology. Then find all solutions to $p(x)=2$ to two decimal places.

Use graphing software to sketch $v(x)=x^4-2x^2+1$. Identify its real zeros and state their multiplicities.

Sketch the graph of $g(x)=(x-1)^2(x+2)$ with technology, then list all x-intercepts and classify the nature of each (crossing or touching).

Using technology, sketch $r(x)=0.5x^4-x^2+2$. Find the coordinates of all turning points and state intervals of concavity.

Sketch $s(x)=x^3-x$ with graphing software. Use it to solve $s(x)=2$ correct to one decimal place.

Use graphing software to sketch $h(x)=x^4-4x^2+1$. Determine its end behavior and approximate real roots to two decimal places.

Sketch $q(x)=x^5-5x^3+4x$ using technology and approximate all its real roots.

Sketch $u(x)=-x^3+4x$ using graphing technology and determine the intervals on which the function is increasing or decreasing.

Use technology to graph $t(x)=x^4-x$ and find all x such that $t(x)=2$ to two decimal places.

Graph $w(x)=2x^5-3x^3+x$ using technology. Approximate the coordinates of its turning points and inflection point.

Use technology to sketch a degree-4 polynomial that has turning points at $(-2,3)$, $(1,-1)$, $(3,5)$ and passes through the origin. Then provide one possible equation.