I've been given f(x) = (x-2)^2 + a

This is the graph that belongs with a = -1

a. What are the coordinates of the top of the graph?

b. How many points of intersection does the graph have when it's a = -1 and y = 5 ?

c. For which values of a does the accompanying graph not share a point with the x-axis?

I've never been able to do these kinds of graph questions, so please do explain, I'm eager to learn :) The original question is in Dutch, so if there are any Dutch people out here~

HeyxJacq Oct 30, 2018

#1**+2 **

a. The top of the graph illustrated has a value of y = 4, so you need to solve the equation (x-2)^{2} - 1 = 4 (this is a quadratic equation and will produce two values for x).

b. Assuming this means the intersection of the curve with the horizontal line at y = 5, there will be two points of intersection.

c. Since 'a' gives the y-coordinate of the vertex (lowest point), then when a>0 the curve will not intyersect the x-axis.

Alan Oct 30, 2018

#1**+2 **

Best Answer

a. The top of the graph illustrated has a value of y = 4, so you need to solve the equation (x-2)^{2} - 1 = 4 (this is a quadratic equation and will produce two values for x).

b. Assuming this means the intersection of the curve with the horizontal line at y = 5, there will be two points of intersection.

c. Since 'a' gives the y-coordinate of the vertex (lowest point), then when a>0 the curve will not intyersect the x-axis.

Alan Oct 30, 2018