Question 1169357
the equation is y = 2x^2 + 4x - 3


this equation is in standard form, where:


a = coefficient of x^2 term.
b = coefficient of x term.
c = constant term.


the vertex is at (x = -b/2a, y = f(-b/2a))


a = 2
b = 4
c = -3


to find the value of x, use the formula:


x = -b/2a


in this equation, b = 4 and a = 2


x = -b/2a becomes x = -b/2a = -4/4 which becomes:


x = -b/2a = -1


to find f(-b/2a), replace x in the quadratic equation with -b/2a.


since -b/2a = -1, replace x with -1 in the equation to get:


y = 2x^2 + 4x - 3 becomes y = 2*(-1)^2 + 4*(-1) - 3


simplify to get y = 2 - 4 - 3


combine like terms to get y = -5


you have x = -1 and y = -5.


the vertex is at (x,y) = (-1,-5).


the following graph of the equation confirms this is true.


<img src = "http://theo.x10hosting.com/2020/110901.jpg">