How do you graph #f(x)=x^2-x+5/4# and identify the x intercepts, vertex?

1 Answer
Jul 8, 2018

#" "#
Vertex: #color(red)((0.5, 1)#

x-intercept: None.

Explanation:

#" "#
We are given the Quadratic equation:

#color(blue)(y=f(x)=x^2-x+5/4#

To draw a graph, create a table of values using the given quadratic function #color(red)(f(x)):#

enter image source here

Using this table, plot the points and draw the graph:

enter image source here

Since the coefficient of the #color(red)(x^2# term is positive, the graph (parabola) will open up and will have a minimum point:

Minimum Point is the Vertex of the Parabola:

enter image source here

From the graph, it is obvious that Vertex (Minimum point) is at: #color(blue)(0.5,1)#

Since the parabola does not intersect the x-axis, the graph does not have an x-intercept.

The parabola passes through the y-axis.

So, y-intercept: : #color(red)(0,1.25)#