The equation of a parabola is given.

y=3/4x^2 − 6x + 15

What are the coordinates of the vertex of the parabola?

Guest Jun 3, 2018

#1**+3 **

For a parabola \(y=ax^2+bx+c\), the vertex's x is equal to \(\frac{-b}{2a}\)

The equation is given to us:

\(y=\frac34x^2 − 6x + 15\\ \)

The x is \(\frac{-(-6)}{2\cdot\frac34}\)

Then you can plug in for y, I hope this helped,

Gavin

GYanggg
Jun 3, 2018

#2**0 **

Yes, that's correct, Gavin!

Continuing, and solving for x, we get: 4

Going back, and plugging our value of 4 for x, we get:

\(y=\frac{3}{4}*4^2-6*4+15=\frac{3}{4}*16-24+15=12-24+15=3\)

Now, we have y=3.

Thus, the coordinates are \(\boxed{(4,3)}\)

tertre
Jun 3, 2018

#3**+3 **

Hey tertre,

The reason I did not fully solve was not because I was lazy.

I wanted to make sure the guest knew what he was doing and understood the solution.

This way, he will actually learn and not just copy the answer we give him.

I was hoping that the guest was going to solve the problem I posed to him, not just receive the answer.

GYanggg
Jun 4, 2018

#4**+2 **

Thanks Gavin,

I know you meant well Tertre but I would like to encourage answerers NOT to give full answers.

If a person gives a part answer, in order to help the asker learn (just as Gavin has done) it is very frustrating when someone comes in and finishes it over the top of them. It diminishes their value as an educator.

We want to help the students learn not just spoon feed them the answers.

If the asker needs more help they should ask for it.

Interactive learning is greatly encouraged!!

Melody
Jun 4, 2018