The curve with equation $y = ax^2 + bx + a$, where $a$ and $b$ are constants, lies completely

Question

The curve with equation $y = ax^2 + bx + a$, where $a$ and $b$ are constants, lies completely above the $x$-axis. Write down the conditions which must apply to $a$ and $b$.[2] Give an example of possible values for $a$ and $b$ which satisfy the conditions in part (i).[2] Using a suitable substitution, explain why the equation $3^{2x-1} = 3^{x+2} - k$ has no solution if $k > 60.75$.[3]

Accepted Answer

(a)(i) $a>0$ and $-2a60.75$.

2023 Ahmad Ibrahim Sec 3 AM EOY Q6

2023 Ahmad Ibrahim Sec 3 AM EOY Q6

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