Question

the graph of the curve y=x^2+bx+c is shown in the figure. Find b and c​

Answer 1

b = - 2, c = - 15

Given data:

The graph of the equation y = x² + bx + c

To find:

The value of b and c

Step-by-step explanation:

The given equation is

y = x² + bx + c ... (1)

From the given diagram, we can say that equation (1) intersects the x-axis at (- 3, 0) and (5, 0).

Satisfying equation (1) by (- 3, 0) and (5, 0), we get

0 = (- 3)² + b (- 3) + c

➜ 0 = 9 - 3b + c

➜ 3b - c = 9 ... (2)

and 0 = 5² + b * 5 + c

➜ 0 = 25 + 5b + c

➜ 5b + c = - 25 ... (3)

Adding (2) and (3), we get

8b = - 16

➜ b = - 2

Putting b = - 2 in (2), we get

3 (- 2) - c = 9

➜ - 6 - c = 9

➜ c = - 6 - 9

➜ c = - 15

Therefore, b = - 2, c = - 15.

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