Question

1. write a quartic function with x-intercepts at -5, 3, -2, and -4 with a y-intercept of 120.
2. write a quartic function with x-intercepts at -4, 5, 7, and -1 with a y-intercept of 200.
3. write a polynomial function with x-intercepts at -2, \\(\frac{1}{2}\\), \\(-\frac{3}{4}\\), and 8 with a y-intercept of (0, 12).
4. convert \\(f(x) = 5(x - 4)(x + 6)(x - 2)\\) to standard form.

x-intercepts: _____________ y-intercept: ___

1. use desmos to determine the x-intercepts of \\(y = 2x^3 + 4x^2 - 70x\\). then, write the function in factored form.
2. use desmos to sketch a graph of \\(f(x) = (x - 3)(x + 6)(2x - 5)\\). label the x-intercepts, y-intercept, local maximum, and local minimum.

Explanation:

Answer:

\( f(x)=-x(x + 5)(x - 3)(x + 2)(x + 4) \)
\( f(x)=-2(x + 4)(x - 5)(x - 7)(x + 1) \)
\( f(x)=-4(x + 2)(2x - 1)(4x + 3)(x - 8) \)
\( f(x)=5x^{3}+10x^{2}-80x + 240 \)
\( y = 2x(x + 7)(x - 5) \)