Answer:
[tex]\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.[/tex]
Step-by-step explanation:
1st boat:
Parabola equation:
[tex]y=ax^2 +bx+c[/tex]
The x-coordinate of the vertex:
[tex]x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a[/tex]
Equation:
[tex]y=ax^2 -2ax+c[/tex]
The y-coordinate of the vertex:
[tex]y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10[/tex]
Parabola passes through the point (-8,1), so
[tex]1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1[/tex]
Solve:
[tex]c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}[/tex]
Parabola equation:
[tex]y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}[/tex]
2nd boat:
Parabola equation:
[tex]y=ax^2 +bx+c[/tex]
The x-coordinate of the vertex:
[tex]x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0[/tex]
Equation:
[tex]y=ax^2+c[/tex]
The y-coordinate of the vertex:
[tex]y_v=a\cdot 0^2+c\Rightarrow c=-7[/tex]
Parabola passes through the point (-8,1), so
[tex]1=a\cdot (-8)^2-7\\ \\64a-7=1[/tex]
Solve:
[tex]a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7[/tex]
Parabola equation:
[tex]y=\dfrac{1}{8}x^2 -7[/tex]
System of two equations:
[tex]\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.[/tex]
Answer:
The answer is A
Step-by-step explanation:
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