Answer:
value of
a = 1
b = 2
c =1
and equation is
y = x² + 2x + 1
Explanation:
Given quadratic equation y = ax² + bx + c
It has y-intercept of (0, 1)
thus, point (0,1) will satisfy equation y = ax² + bx + c.
putting 1 in place of y and 0 in place of x in equation y = ax² + bx + c we have
1 = a*0² + b*0 + c
c = 1
Thus, equation until now is y = ax² + bx + 1
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The parabola also goes through the points (2, 9) and (-5, 16)
point (2, 9) will satisfy equation y = ax² + bx + 1.
putting 9 in place of y and 0 in place of 2 in equation y = ax² + bx + 1 we have
9 = a*2² + b*2 + 1
9 = 4a+2b+1
=>4a+2b = 9-1 = 8
dividing both side by 2 we have
4a/2+2b/2 = 8/2
=> 2a + b = 4
b = 4-2a
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The parabola also goes through the points (2, 9) and (-5, 16)
point (-5, 16) will satisfy equation y = ax² + bx + 1.
putting 9 in place of y and 0 in place of 2 in equation y = ax² + bx + 1 we have
16 = a*(-5)² + b*(-5) + 1
16 = 25a-5b+1
=>25a-5b = 16-1 = 15
dividing both side by 5 we have
25a/5-5b/5 = 15/5
=> 5a - b = 3
second equation is 5a - b = 3
substituting value of b as 4-2a from first equation we have
5a - (4-2a) = 3
=> 5a - 4+2a = 3
=> 7a = 3+4 = 7
=> a = 7/7 = 1
value of b is 4-2a
substituting value of a as 1 in 4 - 2a we have
b = 4 - 2*1 = 4-2 = 2
Thus,
value of
a = 1
b = 2
c =1
and equation is
y = x² + 2x + 1