What is the vertex of the graph y=x^2+3x-4

Expert Answers
samhouston eNotes educator| Certified Educator

Another way of determining the vertex of the graph is by using a graphing calculator.  Graph of y = x^2 + 3x - 4

 

The vertex is (-1.5, -6.25).

If you do not have one, I have included a website that has an online graphing calculator.  Besides vertex points, this website will also calculate x- and y-intercepts.

giorgiana1976 | Student

The vertex of the graph is the extreme point that can be determined in many ways.

I'll use the first derivative method. The roots of the 1st derivative represent the critical points of the function.

f'(x) = 2x + 3

We'll cancel the first derivative:

2x + 3 = 0

x = -3/2

Since the leading coefficient is positive, therefore the vertex of the graph is the minimum point of the function.

f(-3/2) = 9/4 - 9/2 - 4

f(-3/2) = (9-18-16)/4

f(-3/2) = -25/4

The coordinates of the vertex are: V(-3/2 ; -25/4).

atyourservice | Student

`y=x^2+3x-4`

`-b/(2a)`

`a=1` `b=3` `c=-4`

`x=-3/(2(1)) `    `x= -3/2` you can leave this as is or you can divide and get decimals `x=-1.5`

plug it in:

`y=(-3/2)^2+3(-3/2)-4`

`y=-25/4` or `-6.25`

so the vertex can be written as either `(-3/2 , -25/4 )` or  `(-1.5, -6.25)`