Respuesta :
We are given the following quadratic equation
[tex]f(x)=2x^2+7x-10[/tex]The vertex is the maximum/minimum point of the quadratic equation.
The x-coordinate of the vertex is given by
[tex]h=-\frac{b}{2a}[/tex]Comparing the given equation with the general form of the quadratic equation, the coefficients are
a = 2
b = 7
c = -10
[tex]h=-\frac{b}{2a}=-\frac{7}{2(2)}=-\frac{7}{4}=-1.75[/tex]The y-coordinate of the vertex is given by
[tex]\begin{gathered} f(x)=2x^2+7x-10 \\ f(-1.75)=2(-1.75)^2+7(-1.75)-10 \\ f(-1.75)=2(3.0625)^{}-12.25-10 \\ f(-1.75)=6.125^{}-12.25-10 \\ f\mleft(-1.75\mright)=-16.13 \end{gathered}[/tex]This means that we have a minimum point.
Therefore, the minimum point of the given quadratic equation is
[tex](-1.75,-16.13)[/tex]