Question

Find the equation of the parabola y = 2x^2 + bx + c that passes by the points (-1,-5) and ( 2, 10)?

Answer 1

`{\Large \begin{array}{llll} y=2x^2+bx+c \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=-1\\ y=-5 \end{cases}\implies -5=2(-1)^2+b(-1)+c \implies -5=2-b+c \\\\\\ -7=-b+c\implies b-7=c \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=2\\ y=10 \end{cases}\implies 10=2(2)^2+b(2)+c\implies 10=8+2b+c`

`2=2b+c\implies \stackrel{\textit{substituting`

Check the picture below.