Zad. 1
b)
[tex]6 = a*(-2)^2\\3 = 4a /:4\\\frac34=a\\y=\frac34x^2\\\\P_1(2, 3)\\P_2(-2, 3)\\P_3(4, 12)\\P_4(-4, 12)\\P_5(6, 27)[/tex]
c)
[tex]-8=a(-2\sqrt3)^2\\-8=a*4*3\\-8=12a /:12\\\frac{-8}{12}=a\\a=-\frac{4}{6}=-\frac{2}{3}\\y=-\frac23x^2\\\\P_1(3, -6)\\P_2(-3, -6)\\P_3(6, -24)\\P_4(-6, -24)\\P_5(9, -54)\\[/tex]
Zad. 2
[tex]2 = \sqrt{2}*(\sqrt2)^2\\2 \neq 2\sqrt2\\\\2\sqrt{2}= \sqrt2*2^2\\2\sqrt2\neq 4\sqrt2\\\\-2\sqrt2=\sqrt2*(-\sqrt2)\\-2\sqrt2\neq 2\sqrt2\\\\2\sqrt2=\sqrt2*(-\sqrt2)^2\\2\sqrt2=2\sqrt2[/tex]
Odp. D
Zad. 3
Rysunek pogladowy w zalaczniku
[tex]f(x) = \frac23x^2\\6=\frac23x^2/*3\\18=2x^2 /:2\\9=x^2\\x=\sqrt{9}\\x = 3 \\lub\\x = -3[/tex]
A(-3, 6)
B(3, 6)
[tex]|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\|AB|=\sqrt{(3+3)^2+(6-6)^2}\\|AB|=\sqrt{6^2}\\|AB = 6[/tex]
Zad. 4
[tex]y=\frac34*1^2\\y=\frac34*1\\y=\frac34\\A = (1; \frac34)\\\\y=-\frac76*1^2\\y=-\frac76*1\\y=-\frac76\\B=(1, -\frac76)\\\\|AB|=\sqrt{(1-1)^2+(-\frac76-\frac34)^2}\\|AB|=\sqrt{(-\frac{14}{12}-\frac{9}{12})^2}\\|AB| = \sqrt{(-\frac{23}{12})^2}\\|AB| = \frac{23}{12}[/tex]
Odp. D
