Find a formula for the function described. A fourth-degree polynomial whose graph is symmetric about the y-axis, has a y-intercept of 0, and global ma

naivlingr

naivlingr

Answered question

2021-05-13

Find a formula for the function described. A fourth-degree polynomial whose graph is symmetric about the y-axis, has a y-intercept of 0, and global maxima at (1, 2) and (-1, 2).

Answer & Explanation

Arham Warner

Arham Warner

Skilled2021-05-14Added 102 answers

The common polynomial of fourth degree:  p(x)=ax4+bx3+cx2+ dx +e
Terms with odd powers of x must be zero because the graph is symmetric about the y-axis ⇒b=d=0. The y-intercept: y(0)=e=0e=0
Reduced polynomial so far: p(x)=ax4+cx2.
Critical points: p(x)=4ax3+2cxp(x)=2x(2ax2+c)
Critical areas (aside from x=0): x=±c2a We have these two equations: 1=c2a
a+c=2
Solving these gives a=-2 and c=4. Resulting polynomial: P(particular)=2x4+4x2

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