First slide

Theory of expressions

Question

The graph of the quadratic trinomial $y = {ax}^{2} + bx + c$ has its vertex at (4, -5) and two x-intercepts, one positive and one negative. Which of the following holds good?

Moderate

A

a > 0
B

b < 0
C

c < 0
D

8a = b

Solution

From figure,
a > 0
$- \frac{b}{2 a} = 4 or - \frac{b}{2 a} > 0$
$\begin{array}{ll} ∴ b < 0 \\ f (0) = c < 0 \end{array}$
Also, $- \frac{b}{2 a} = 4 or 8 a + b = 0$

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