Polynomial graphs and how the sign of the leading coefficient affects the broad shape of cubic and quartic graphs, and how real roots appear as x-intercepts where the curve touches or crosses the axis depending on whether the root is repeated or unique.
The coefficient a of the leading term (the one with the highest ) determines the broad shape of its graph:
Cubic
Quartic
The curve of a polynomial touches the x-axis at each real root. The shape of the curve at these points depends on whether the root is unique or repeated:
Nice work completing Polynomial graphs, here's a quick recap of what we covered:
Exercises checked off
Polynomial graphs and how the sign of the leading coefficient affects the broad shape of cubic and quartic graphs, and how real roots appear as x-intercepts where the curve touches or crosses the axis depending on whether the root is repeated or unique.
The coefficient a of the leading term (the one with the highest ) determines the broad shape of its graph:
Cubic
Quartic
The curve of a polynomial touches the x-axis at each real root. The shape of the curve at these points depends on whether the root is unique or repeated:
Nice work completing Polynomial graphs, here's a quick recap of what we covered:
Exercises checked off