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

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 3E

See similar textbooks

Related questions

Question

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 $y = a x^{3} + b x^{2} + c x + d$ .

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

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Interpolation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage