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Sagot :
EXPLANATION
Since we need to find the vertex of the parabola, we first should calculate the params (h,k), as shown as follows:
[tex]h=-\frac{b}{2a}\text{ k=f(h)}[/tex]As the general form is as follows:
[tex]f(x)=ax^2+bx+c[/tex]We have that a=-4.9, b=2.8 and c=15
Computing the value of h:
[tex]h=-\frac{2.8}{2\cdot(-4.9)}[/tex]Multiplying numbers:
[tex]h=\frac{2.8}{9.8}=0.28571\ldots[/tex]Now, we need to compute the value of k:
[tex]k=-4.9\cdot\: 0.28571\ldots^2+2.8\cdot\: 0.28571\ldots+15[/tex]Multiplying numbers:
[tex]=-0.28571\ldots^2\cdot\: 4.9+0.8+15[/tex]Adding numbers:
[tex]=15.8-0.28571\ldots^2\cdot\: 4.9[/tex][tex]=15.8-0.4[/tex][tex]\mathrm{Subtract\: the\: numbers\colon}\: 15.8-0.4=15.4[/tex][tex]=15.4[/tex][tex]k=15.4[/tex]Therefore, the parabola vertex is (h,k) = (0.2857,15.4)
Thus, the equation of the parabola in vertex form is as follows:
[tex]f(x)=-4.9(x-0.2857)^2+15.4[/tex]
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