5.) 4 cubic equation C degree 3 polynomialy2 goes th dugh the Sbints.ax3+bx2+(x'+d(,),0,5), (2,equation usingand (33%). Find the cebicyourlertey

Answered: 5.) 4 cubic equation Cdegree 3…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 17RE

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5.) 4 cubic equation C degree 3 polynomial
y2 goes th dugh the Sbints.
ax3+bx2+(x'+d
(,),0,5), (2,
equation using
and (33%). Find the cebic
yourlertey

Expert Solution

Step 1

The given points are $(- 2, 1), (0, 5), (2, 9) a n d (3, 36)$ .

The general form of the cubic equation is $y = a x^{3} + b x^{2} + c x + d$ .

Substitute the point $(0, 5)$ in $a x^{3} + b x^{2} + c x + d = y$ .

$\begin{array}{rcl} a {(0)}^{3} + b {(0)}^{2} + c (0) + d & = & 5 \\ 0 + d & = & 5 \\ d & = & 5 \end{array}$

Substitute the point $(- 2, 1)$ and d=5 in $y = a x^{3} + b x^{2} + c x + d$ .

$\begin{array}{rcl} a {(- 2)}^{3} + b {(- 2)}^{2} + c (- 2) + 5 & = & 1 \\ - 8 a + 4 b - 2 c + 5 & = & 1 \\ - 8 a + 4 b - 2 c & = & 1 - 5 \\ - 8 a + 4 b - 2 c & = & - 4 \dots (1) \end{array}$

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