Question 949386
h(x) = x^2 + x + 5
the vertex of a quadratic equation is given by the formula of x = -b/2a
in the quadratic equation of x^2 + x + 5, which is in standard form, and has to be in standard form in order for the formula to work, you get:


a = 1
b = 1
c = 5


a is the coefficient of the x^2 term.
b is the coefficient of the x term.
c is the constant term.


in the formula of x = -b/2a, replace b with 1 and a with 1 to get:


x = -1/2


when x = -1/2, h(x) = x^2 + x + 5 becomes 1/4 - 1/2 + 5 which becomes h(x) = 4 and 3/4.


the coordinates of the vertex are (x,y) = (-1/4, 4 and 3/4).


the graph of the equation is shown below:


{{{graph(600,600,-10,10,-10,10,x^2 + x + 5)}}}


you can see from the graph that the vertex is at x = -1/2 and y = 4 and 3/4.


draw an imaginary vertical line through the vertex and the x-axis, and an imaginary horizontal line through the vertex and the y-axis, and it will be easier to see.