IB Mathematics Applications & Interpretation Question Type 7: Sketching Graphs of Polynomials Using Technology Exercises

Sketch the graph of $q(x)=x^5-5x^3+4x$ 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.

Sketch the graph of $h(x)=x^4-4x^2+1$. Determine its end behavior and find the real roots, correct to two decimal places.

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

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

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

Sketch the graph of $s(x)=x^3-x$ for $-2\le x\le 2$. Use your graph to solve the equation $s(x)=2$, giving your answer correct to one decimal place.

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).

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

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