第3章 3.15

y=ax2+3x4=a(x2+3ax)4=a(x+32a)294a4y = ax^2 + 3x - 4 = a\left(x^2 + \dfrac{3}{a}x\right) - 4 = a\left(x + \dfrac{3}{2a}\right)^2 - \dfrac{9}{4a} - 4

y=2x26x+b=2(x23x)+b=2(x32)292+by = 2x^2 - 6x + b = 2(x^2 - 3x) + b = 2\left(x - \dfrac{3}{2}\right)^2 - \dfrac{9}{2} + b

頂点が一致するので

32a=32a=1\dfrac{3}{2a} = -\dfrac{3}{2} \qquad a = -1

94a4=92+b944=92+bb=114-\dfrac{9}{4a} - 4 = -\dfrac{9}{2} + b \qquad \dfrac{9}{4} - 4 = -\dfrac{9}{2} + b \qquad b = \dfrac{11}{4}

これから

a=1、 b=114a = -1、\ b = \dfrac{11}{4}

解説: r31bn1z