Respuesta :
First, let's remember what the axis of symmetry means.
The axis of symmetry is a line that splits our parabola in half. This line also has a very interesting property: The vertex belongs to this line.
(illustrative example. Not the given parabola)
Now, for the particular parabola we're given, we know that this axis of symmetry is:
[tex]x=-\frac{4}{5}[/tex]Notice that, taking into account what we already know about the defnition of the axis of symmetry, we can conclude that this is the x-coordinate of the vertex.
To find the corresponding y-value, we just plug it in the formula of our parabola:
[tex]\begin{gathered} y=5x^2+8x-13 \\ \\ \rightarrow y=5\cdot(-\frac{4}{5})^2+8\cdot(-\frac{4}{5})-13 \\ \\ \rightarrow y=5\cdot(-\frac{4}{5})^{}\cdot(-\frac{4}{5})+8\cdot(-\frac{4}{5})-13 \\ \\ \rightarrow y=5\cdot(\frac{16}{25})^{}+8\cdot(-\frac{4}{5})-13 \\ \\ \rightarrow y=\frac{16}{5}^{}-\frac{32}{5}-13 \\ \\ \rightarrow y=\frac{16}{5}^{}-\frac{32}{5}-\frac{65}{5} \\ \\ \rightarrow y=\frac{16-32-65}{5}^{} \\ \\ \Rightarrow y=-\frac{81}{5} \end{gathered}[/tex]Therefore, we can conclude that the y-coordinate of our vertex is:
[tex]y=-\frac{81}{5}[/tex](Given parabola, with its axis of symmetry and vertex highlighted)
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