Question

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = 4x2 + 5x – 1.

Answer 1

Hello!

The answer is:

- The vertex of the parabola is located on the point (-0.625,-2.563)

- The axis of symmetry of the parabola is:

$x=-0.625$

Why?

To solve the problem, we need to remember the standard form of the equation of the parabola:

$y=ax^{2} +bx+c$

Also, we need to remember the way to find the vertex of the parabola.

We can find using the following formula

$x=\frac{-b}{2a}$

Then, we need to substitute "x" into the equation of the parabola to find the "y" value.

Also, we can find the axis of symmetry of a parabola with the same equation that we found the "x-coordinate" of the vertex, since in that coordinate is located the vertical line that divides the parabola into two symmetic pats (axis of symmetry).

So, we are given the parabola:

$y=4x^{2} +5x-1$

Where,

$a=4\\b=5\\c=-1$

Then,

Finding the vertex, we have:

$x=\frac{-b}{2a}\\\\x=\frac{-5}{2*(4)}=\frac{-5}{8}=-0.625$

Now, substituting the x-coordinate value into the equation of the parabola to find the y-coordinate value, we have:

$y=4(-0.625)^{2} +5(-0.625)-1$

$y=4*(0.39)-3.13-1=-2.563$

Then, we know that the vertex of the parabola is located on the point (-0.625,-2.563)

Also, we know that the axis of symmetry of the parabola is:

$x=-0.625$

Have a nice day!