Question

Question open for 27 mins.

Answer 1

How do I find the vertex and axis of symmetry of: y=-2x^2+28x-18

Answer 2

@mathstudent55

Answer 3

two ways.
1) "complete the square" so that you can write the equation in vertex form
y = a( x-h)^2 +k
x=h is the axis of symmetry

2) use x= - b/(2a)
where a, b, (and c but we don't use it) are from matching your equation to
y = a x^2 + b x + c

Answer 4

hint:
the x-coordinate of the symmetry axis, is:
\[\Large {x_V} = - \frac{b}{{2a}} = - \frac{{28}}{{2 \times \left( { - 12} \right)}} = ...?\]

Answer 5

more precisely, it is the equation of the symmetry axis and the x-.coordinate of the vertex of the parabola

Answer 6

-7/6

Answer 7

I got \(7/6\)

Answer 8

so, the equation of the symmetry axis, is:
\[\Large x = \frac{7}{6}\]
and the x-coordinate of the vertex of the parabola, is:
\[\Large {x_V} = \frac{7}{6}\]

Answer 9

now, in order to get the y-coordinate of the vertex of parabola, we have to replace \(x=7/6\) into the equation of parabola

Answer 10

so, we have to compute this:
\[\Large \begin{gathered}
{y_V} = - 2{x^2} + 28x + 18 = \hfill \\
\hfill \\
= - 2 \cdot {\left( {\frac{7}{6}} \right)^2} + 28 \cdot \left( {\frac{7}{6}} \right) + 18 = ...? \hfill \\
\end{gathered} \]

Answer 11

oops.. it is -18:
\[\Large \begin{gathered}
{y_V} = - 2{x^2} + 28x - 18 = \hfill \\
\hfill \\
= - 2 \cdot {\left( {\frac{7}{6}} \right)^2} + 28 \cdot \left( {\frac{7}{6}} \right) - 18 = ...? \hfill \\
\end{gathered} \]

Answer 12

\[\frac{ 215 }{ 18 }\]

Answer 13

that's right!
so the vertex is the subsequent point:
\[\Large V = \left( {\frac{7}{6},\frac{{215}}{{18}}} \right)\]

Answer 14

I'm very sorry, I have made a typo, here is the x-coordinate of the vertex:
\[\Large {x_V} = - \frac{b}{{2a}} = - \frac{{28}}{{2 \times \left( { - 2} \right)}} = 7\]

Answer 15

since the first coefficient it is \(-2\) and not \(-12\)

Answer 16

so the y-coordinate of the vertex, is:
\[\Large \begin{gathered}
{y_V} = - 2{x^2} + 28x - 18 = \hfill \\
\hfill \\
= - 2 \cdot {\left( 7 \right)^2} + 28 \cdot \left( 7 \right) - 18 = 80 \hfill \\
\end{gathered} \]

Answer 17

namely:
\[\huge V = \left( {7,80} \right)\]

Answer 18

Correct :)

Answer 19

:)
and the equation of the axis of symmetry, is, of course:

\(\huge x=7\)