Question

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

Answer 1

To find the x value of the vertex we do:

x =
`(-b)/(2a)`
if your quadratic function is in the form ax² + bx + c = y

x =
`(-3)/(2(1))`
x =
`(-3)/(2)`

Now we plug this x into the equation and solve for y.

y =
`((-3)/(2)) ^(2) + 3( (-3)/(2) ) + 4`
y =
`(9)/(4) - (9)/(2) + 4`
y =
`(9)/(4) - (18)/(4) + 4`
y =
`(-9)/(4) + 4`
y =
`(-9)/(4) + (16)/(4)`
y =
`(7)/(4)`

Your vertex (if my math is correct) is at
`( (-3)/(2), (7)/(4) )`