Algebra homework

Question

1.For the inequality y≥1/2(x-3)^2+1, identity the following.

Vertex -

Intercepts -

Does the graph flip up or down ?

2.Identify whether the graph of the line will be dashed or solid.

Answer 1

You did not put in brackets which leaves some ambiguity in how to parse the RHS. I am guessing that the 1/2 factor can be read as 0.5 i.e. it is just a coefficient of the x term.

To simplify the problem, you can first think about what is happening in

y = 0.5 (x - 3)^2 + 1.

This is an equation of a parabola which is symmetric about x = 3 and is curved upwards i.e. x = 3, y = 1 is the minimum point. The parabola does not touch the x axis so we can look for intersections with y axis. To do that, put x = 0 (equation for y axis) in the above equation and solve for y.

Finally put the inequality back, y >= 0.5 (x - 3)^2 + 1. This means that solution are all points living on the graph and above it. For <=, it would be all points on the graph and below it. If = is remove, then the points on the graph are excluded etc.

Answer 2

Hi there Leah! I would love to help you out.

this graph is in vertex form. To find the vertex we can use the following expression:

a(x - h)^2 + k

h is the x-value of the vertex (make sure you change the sign to be the opposite of what it is in the equation) and K is the y-value of the vertex (keep the sign the same). Here is the inequality given to us:

y≥1/2(x-3)^2+1

the h value in this case is 3 and the k is 1. So our vertex is (3,1)

To find out if the graph is flipped up or down we look at our “a” in the form:

a(x - h)^2 + k

if the a is positive, it opens up. If it is negative, it opens down. In our inequality, the value of a is positive 1/2 so our grap will open up.

Lastly, to determine whether the line is dashed or solid, we look at the inequality symbol. If it is < or > (it doesn’t have the or equal to symbol) it is dashed. If it is ≤ or ≥ (it does have the or equal to symbol) it is solid. Since our inequality has the or equal to symbol, it is a solid line.

i hope this explanation was thorough and answered all of your questions. If you have additional questions please don’t hesitate to reach out. Learn on! :)