I need a step by step walkthrough on finding the y-coordinate of the vertex of a quadratic equation. This is the equation:5x^2 +8x -13Things I already know:a= 5b= 8c= -13x= -4/5The axis of symmetry is -4/5.I need a very clear, easy to understand answer.

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)

Ver imagen MalonnaY692951
Ver imagen MalonnaY692951
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