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**Macleef** Determine a quadratic function $\displaystyle f(x) = ax^2 + bx + c$ whose graph passes through the point $\displaystyle (2, 19)$ and that has a horizontal tangent at $\displaystyle (-1, -8)$.

**My work: **

$\displaystyle y = mx + b$

$\displaystyle 19 = -1(2) + b$

$\displaystyle 19 + 2 = b$

$\displaystyle 21 = b$

$\displaystyle -8 = a(2)^2 + b(2) + 21$

$\displaystyle -8 = 4a + 2b + 21$

$\displaystyle -29 = 4a + 2b$

I don't know what to do now? I'm not even sure I'm on the right track. Please show me the solution step by step?

**Textbook Answer:** $\displaystyle f(x) = 3x^2 + 6x - 5$

Note: I'm just beginning to learn derivatives...