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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

Best Answer 

 #1
avatar+27128 
+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
avatar+27128 
+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

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