Consider the function y = - x^{4} + 4
Determine the leading coefficient of the polynomial function.
Is the degree of the polynomial odd or even?
Does the curve rise or fall to the left?
Does the curve rise or fall to the right?
Sketch the graph of y = - x^{4} + 4.
For each of the following functions:
Find the x-intercepts.
Find the y-intercept.
Sketch the graph.
The graph of y = P \left(x\right) is shown. Plot the graph of y = - P \left(x\right).
Consider the function y = - \left(x - 1\right)^{4} + 3.
As x \to -\infty, what does y approach?
As x \to \infty, what does y approach?
What is the y-intercept of the function?
Sketch the graph of the function.
Consider the function y = \left(x - 1\right)^{4} - 3.
As x \to -\infty, what does y approach?
As x \to \infty, what does y approach?
What is the y-intercept of the function?
Sketch the graph of the function.
Sketch the graph of the function f \left( x \right) = 2 \left(x - 1\right)^{4} - 2.
Consider the curve y = 4 \left(x + 3\right)^{4} - 64.
Find the x-intercepts.
Find the y-intercept.
By how many units has the original power function y = 4(x+3)^4 been translated vertically down to get the above function?
Sketch the graph of the function.
Consider the curve y = - 3 \left(x - 2\right)^{4} + 32.
Find the x-intercept(s) in exact form.
Find the y-intercept.
By how many units has the original power function y = -3x^4 + 32 been translated horizontally to the right to get the above function?
Sketch the graph of the function.
Consider the curve y = - 81 \left(x - 5\right)^{4} + 16.
Find the x-intercepts.
Find the y-intercept.
What is the vertical dilation factor from the original power function y = (x-5)^4?
Sketch the graph of the function.
For each of the following graphs of quartic functions in the form y = a\left(x-h\right)^4 + k:
State the coordinates of the turning point.
State the equation for the quartic function.
For each of the following graphs of quartic functions find the equation of the graph in factored form:
Find the equations of the following quartic functions, given the graph of the function:
Cuts through the x-axis when x=2, -1, -5 and \dfrac{2}{3} and has a y-intercept of \left(0,10\right).
Cuts through the x-axis at \left(-4,0\right) and \left(1,0\right), touches at \left(2,0\right) and has a y-intercept of \left(0,6\right).
Has stationary point of inflection at \left(3, 0\right), cuts through the x-axis at \left(8,0\right) and has a \\y-intercept of \left(0, 12\right).