Question

Find the vertex of this parabola:
y = -2x2 + 4x + 1
can someone help will give medal

Answer 1

the vertex V of a parabola has the subsequent coordinates:
\[\Large V = \left( { - \frac{b}{{2a}}, - \frac{{{b^2} - 4ac}}{{2a}}} \right)\]
where the coefficients a, b, and c are such that:
y=ax^2+bx+c

Answer 2

thanks

Answer 3

please wait,I have made a typo, the rightformula is:
\[\Large V = \left( { - \frac{b}{{2a}}, - \frac{{{b^2} - 4ac}}{{4a}}} \right)\]

Answer 4

what do i do for the commas

Answer 5

-8,8

Answer 6

so we have:
\[\Large \begin{gathered}
- \frac{b}{{2a}} = - \frac{4}{{2 \times \left( { - 2} \right)}} = ...? \hfill \\
\hfill \\
- \frac{{{b^2} - 4ac}}{{4a}} = - \frac{{16 - 4 \times \left( { - 2} \right) \times 1}}{{4 \times \left( { - 2} \right)}} = ...? \hfill \\
\end{gathered} \]

Answer 7

wait -1,-8

Answer 8

more explanation:
the x-ccordinate of the vertex is:
\[ - \frac{b}{{2a}} = - \frac{4}{{2 \times \left( { - 2} \right)}} = ...?\]
whereas the y-coordinate of the vertex is:
\[ - \frac{{{b^2} - 4ac}}{{4a}} = - \frac{{16 - 4 \times \left( { - 2} \right) \times 1}}{{4 \times \left( { - 2} \right)}} = ...?\]
usually we separate those coordinates, by a comma, like this:
\[V = \left( {x,y} \right)\]

Answer 9

-1,-1

Answer 10

we have:
\[ - \frac{b}{{2a}} = - \frac{4}{{2 \times \left( { - 2} \right)}} = \frac{4}{4} = 1\]

Answer 11

whereas:
\[ - \frac{{{b^2} - 4ac}}{{4a}} = - \frac{{16 - 4 \times \left( { - 2} \right) \times 1}}{{4 \times \left( { - 2} \right)}} = - \frac{{24}}{{ - 8}} = 3.\]

Answer 12

so we can write:
\[V = \left( {x,y} \right) = \left( {1,3} \right)\]

Answer 13

ohhh ok i get thanks for helping me

Answer 14

thanks!