The graph shows the solution of the following system of equations. y = –5∕3x + 3 y = 1∕3x

For the graph, identify the axis of symmetry, vertex, y-intercept, max/min, and domain and range

kirill [66]

In the present problem, it is presented a figure of a graph of a parabola with concavity facing up, what implies in that the graph will not have a Max., but a Min. value, and it is in the vertex.

Let us start with the A.O.S. (Axis Of Symmetry). For a parabola, it is the line that passes in the minimum point, that can be identified in the present figure as being in the x = - 1 point. And for this reason, we are able to answer the first part as:

A.O.S.: x = -1

Now, as mentioned above, the vertex lies in the minimum point, which is located in the x = -1 and with height y = 2. This allow us to answer the second part as:

Vertex: (-1, 2)

About the y-interception, it happens when the graph passes through the y-axis. It happens when x = 0, and the answer is just the value of Y where the graph assumes x=0, which is at:

Y-intercept: y = 4

Because the parabola has concavity facing up, the graph presents a value of minimum, but no maximum. And this is possible to be identified as the point where x = -1 and y = 2, which lead us to the following answer for the third part of the question:

Min.: (-1 , 2)

The domain for any second-order polynomial is the entire real number because there is no restriction for the value of x. And for this reason, the answer of the fourth part of the answer is:

Domain: All real numbers

About the range, for a parabola with the concavity facing up, it can be determined as all the real numbers bigger or equal to the minimum value of the function, which is y = 2. From this reason, we are able to answer the last part of the question as:

Range: All real numbers ≥ 2

8 0

6 months ago

Is 2a * b = a^2 + b^2 true or false

alisha [4.7K]

First step of the equation is to simplify the equation 2a • b = a2 + b2 into 2 ab = a2 + b2. This cannot be factored anymore although. when we try to substitute a with 5 and b with 2, the answer in the right hand side of the equation is -9. hence the answer to this problem is false. we can try another values to verify.

5 0

2 years ago

At a football championship game,the home team gave a football to each of the first 100 fans who arrived at the stadium. How much

Ilia_Sergeevich [38]

What grade level is this

5 0

3 years ago

Read 2 more answers

The brand manager for a brand toothpaste must plan a campaign designed to increase brand recognition. He wants to first determin

bulgar [2K]

We need to find out how many adults must the brand manager survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage.

From the given data we know that our confidence level is 90%. From Standard Normal Table we know that the critical level at 90% confidence level is 1.645. In other words, $Z_{Critical}=1.645$ .

We also know that E=5% or E=0.05

Also, since, $\hat{p}$ is not given, we will assume that $\hat{p}$ =0.5. This is because, the formula that we use will have $\hat{p}(1-\hat{p})$ in the expression and that will be maximum only when $\hat{p}$ =0.5. (For any other value of $\hat{p}$ , we will get a value less than 0.25. For example if, $\hat{p}$ is 0.4, then $1-\hat{p}=0.6$ and thus, $\hat{p}(1-\hat{p})=0.24$ .).