1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# The graph of an equation is given above. Identify the polynomial satisfying the graph?

A
y=x2+2
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B
y=x2
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C
y=x2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
y=x22
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is C y=x2Given: The graph of an equation with four points, (-2, 4), (-1, 1), (2, 4), (1, 1)To find the degree of the polynomialSol: As there are 4 points, the function becomesy=ax3+bx2+cx+dReplace x and y with the coordinate values given to get the system:(−2,4)⟹4=a(−2)3+b(−2)2+c(−2)+d⟹4=−8a+4b−2c+d....(i)(−1,1)⟹1=a(−1)3+b(−1)2+c(−1)+d⟹1=−a+b−c+d.........(ii)(2,4)⟹4=a(2)3+b(2)2+c(2)+d⟹4=8a+4b+2c+d........(iii)(1,1)⟹1=a(1)3+b(1)2+c(1)+d⟹1=a+b+c+d...........(iv)(i)+(iii), we get8b+2d=8⟹4b+d=4...(v)(ii)+(iv), we get2b+2d=2⟹b+d=1.......(vi)(v)−(vi), we get3b=3⟹b=1Substituting the value of b in equation (vi) we getd=0Substituting the value of b and d in equation (iii) and (iv), we get the following new set of equation,8a+4(1)+2c+0=4⟹8a+2c=0..(vii)a+1+c+0=1⟹a+c=0.......(viii)(vii)−[2×(viii)], we get6a=0⟹a=0Substituting the value of a in equation (viii), we getc=0Hence, the equation for the given graph is y=0(x3)+(1)x2+(0)x+0⟹y=x2Therefore the degree of the polynomial is 2

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Graphical Interpretation of Differentiability
MATHEMATICS
Watch in App
Join BYJU'S Learning Program