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=(-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=(-b)/(2a)\\\\x=(-5)/(2*(4))=(-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!