We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

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