Respuesta :
Answer:
[tex]A=3[/tex]
Explanation: We are given two points, P1 is vertex and P2 is another point on the parabola:
[tex]\begin{gathered} P_1(2,-4) \\ P_2(3,-1) \end{gathered}[/tex]The general form of the equation of a parabola is:
[tex]y(x)=A(x\pm B)^2+C[/tex]Where A is the Coefficient of the parabola function which is responsible for compression and stretch, likewise B is responsible for the translation along the x-axis and C is responsible for translation along the y-axis.
We know that our function is translated 2 units towards the right and 4 units downwards:
Therefore:
[tex]\begin{gathered} B=-2 \\ C=-4 \end{gathered}[/tex]And this turns the parabola equation into:
[tex]y(x)=A(x-2)^2-4[/tex]Using P2 we can find the constant-coefficient as:
[tex]\begin{gathered} y(x)=A(x-2)^2-4_{} \\ P_2(3,-1) \\ \\ \\ \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} y(3)=A(3-2)^2-4=-1\rightarrow A-4=-1 \\ \because\rightarrow \\ A=3 \end{gathered}[/tex]