a) We want to check if the graph is concave up or down
As we can see, the value of a is greater than zero
What that means is that the graph opens up and thus it is concave up
b) We want to get the value of the axis of symmetry
Mathematically, we have this as;
[tex]\begin{gathered} x\text{ = }\frac{-b}{2a} \\ \\ a\text{ = 4, b = 3} \\ \\ x\text{ = }\frac{-3}{2(4)}=\text{ }\frac{-3}{8} \\ \\ x\text{ = }\frac{-3}{8}\text{ } \end{gathered}[/tex]
c) Vertex
[tex]\begin{gathered} \text{The vertex form is;} \\ a(x-h)^2\text{ + }k \\ \text{where vertex is (h,K)} \\ So,\text{ we have;} \\ 4x^2+3x-7\text{ as } \\ 4(x+\frac{3}{8})^2-\frac{121}{16} \\ \\ So,\text{ vertex is (}\frac{-3}{8},\frac{-121}{16}) \end{gathered}[/tex]
d)
