I cannot find an example and am confused about what to do with this problem. Can someone tell me what they want? Do they want me to graph the function and determine x&f? I am just not sure how to get my answer.
My problem is:
Compare the graph of the given quadratic function f and the graph of y=x2.
f(x)=(x-2)2+3
I expect that you mean y = x^2 and
f(x) = (x-2)^2 + 3. We suggest you to use a ^ before all exponents to help us understand what you are writing.
Both curves are parabolas that open upward. The first one, "y" has its minimum value when x = 0, and the y value there is y = 0.
The second curve, f(x), has its minimum value at x = 2, and the y value there is f(x) = 3. One curve looks like the other, except that they are displaced to different regions of the graph.
If they are suppose to be exponents, that would make more sense. But my problem was written exactly as I typed it. So the answers they are looking for are the values of x, y, and f(x)? Thank-you for your help.
3x + 24y = 24 and 27x – 15y = -15
how do i solve using substitution method
In order to compare the graph of the quadratic function f(x)=(x-2)2+3 and the graph of y=x2, you need to understand how to graph quadratic functions and determine the key characteristics of the graphs.
To graph a quadratic function, here are the steps you can follow:
1. Identify the key features: The standard form of a quadratic function is y = ax^2 + bx + c, where:
- a represents the coefficient of the x^2 term,
- b represents the coefficient of the x term,
- c represents the constant term.
2. Determine the vertex: The vertex is the highest or lowest point of the parabola, and it can be found using the formula: x = -b/2a. The y-coordinate of the vertex can be found by substituting the x-value of the vertex into the function.
3. Find the y-intercept: The y-intercept is the point where the graph intersects the y-axis. It can be found by substituting x = 0 into the function.
4. Determine the x-intercepts: The x-intercepts are the points where the graph intersects the x-axis. They can be found by solving the quadratic equation ax^2 + bx + c = 0.
5. Sketch the graph: Based on the information obtained from the previous steps, sketch the parabola using the vertex, y-intercept, and x-intercepts.
Now, let's apply these steps to compare the graphs of f(x)=(x-2)2+3 and y=x^2:
1. Identify the key features:
- For f(x)=(x-2)2+3:
- a = 1,
- b = -4,
- c = 7.
2. Determine the vertex:
The x-coordinate of the vertex can be found using x = -b/2a:
x = -(-4)/(2*1) = 2.
To find the y-coordinate of the vertex, substitute x = 2 into the function:
y = (2-2)2 + 3 = 3.
Therefore, the vertex of f(x)=(x-2)2+3 is (2, 3).
3. Find the y-intercept:
Substitute x = 0 into the function:
y = (0-2)2 + 3 = 7.
Therefore, the y-intercept is (0, 7).
4. Determine the x-intercepts:
Set y = 0 in the quadratic equation:
(x-2)2 + 3 = 0.
Solve this equation to find the x-intercepts, if any.
5. Sketch the graph:
Based on the obtained information, sketch the graph of f(x)=(x-2)2+3 using the vertex, y-intercept, and x-intercepts (if applicable).
To compare this graph with the graph of y=x^2, plot the graph of y=x^2 on the same coordinate axis using the same steps outlined above. By comparing the two graphs, you can analyze their similarities and differences, including their shapes, positions, and key features.