y=4x²+bx+c
A(3;2)
Формулы координат вершины параболы:
[tex]x _{o} = - \frac{b}{2a} \\ 3 = - \frac{b}{2 \times 4} \\ 3 = - \frac{b}{8} \\ b = - 8 \times 3 \\ b = - 24 \\ \\ y_{o} = - \frac{ {b}^{2} - 4ac }{4a} \\ 2 = - \frac{( - 24) {}^{2} - 4 \times 4c }{4 \times 4} \\ 576 - 16c = - 16 \times 2 \\ 576 - 16c = - 32 \\ 16c = 576 + 32 \\ 16c = 608 \\ c = 608 \div 16 \\ c = 38[/tex]
Ответ: b = - 24 ; c = 38
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Verified answer
y=4x²+bx+c
A(3;2)
Формулы координат вершины параболы:
[tex]x _{o} = - \frac{b}{2a} \\ 3 = - \frac{b}{2 \times 4} \\ 3 = - \frac{b}{8} \\ b = - 8 \times 3 \\ b = - 24 \\ \\ y_{o} = - \frac{ {b}^{2} - 4ac }{4a} \\ 2 = - \frac{( - 24) {}^{2} - 4 \times 4c }{4 \times 4} \\ 576 - 16c = - 16 \times 2 \\ 576 - 16c = - 32 \\ 16c = 576 + 32 \\ 16c = 608 \\ c = 608 \div 16 \\ c = 38[/tex]
Ответ: b = - 24 ; c = 38