Weber Schneider
02/05/2023 · Primary School
Instructions: For each given polynomial function, determine the following and sketch the graph. \( f(x)=-x^{4}+10 x^{2}-9 \). \( y=x^{2}(x+5)(x-4) \) a. Sign of the leading coefficient: b. degree of the function: c. \( x \)-intercepts: d. y-intercept: e. number of turning points:- f. Sketch the graph
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For \( f(x) = -x^4 + 10x^2 - 9 \):
a. The leading coefficient is negative.
b. The degree is 4.
c. The \( x \)-intercepts are at \( x = -3, -1, 1, 3 \).
d. The \( y \)-intercept is at \( y = -9 \).
e. There are 3 turning points.
For \( y = x^2(x + 5)(x - 4) \):
a. The leading coefficient is positive.
b. The degree is 4.
c. The \( x \)-intercepts are at \( x = 0 \) (multiplicity 2), \( x = -5 \), and \( x = 4 \).
d. The \( y \)-intercept is at \( y = 0 \).
e. There are 3 turning points.
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