Figure 2.23 shows the graph of the polynomial f(x) = ax² + bx + c for which
A. a < 0, b > 0 and c > 0
B. a < 0, b < 0 and c > 0
C. a < 0, b < 0 and c < 0
D. a > 0, b > 0 and c < 0
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B. a < 0, b < 0 and c > 0
Step-by-step explanation:
f(x) = ax² + bx + c is a parabola that opens downwards. So a < 0.
The parabola cuts the Y-axis at P which lies on OY. When x is 0, y = c. So the co-ordinates of P are (0,c). P lies on OY. So C > 0.
The vertex -b/2a, -D/4a of the parabola lies in Quadrant II. So -b/2a implies b < 0.
Therefore a < 0, b < 0 and c > 0.
Option B is the answer.
Please find attached the graph.
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