The school band is comprised of middle school students and high school students, but it always has the same maximum capacity. La
1 answer:
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Answer:
<em>Maximum: (-1,9)</em>
Step-by-step explanation:
<u>Vertex form of the quadratic function</u>
If the graph of the quadratic function has a vertex at the point (h,k), then the function can be written as:
Where a is the leading coefficient.
We are given the following function:
To find the vertex, we need to complete squares. First, factor -2 on the first two terms:
The expression in parentheses must be completed to represent the square of a binomial. Adding 1 and subtracting 1:
Taking out the -1:
Factoring the trinomial and operating:
Comparing with the vertex form we have
Vertex (-1,9)
Leading coefficient: -2
Since the leading coefficient is negative, the function has a maximum value at its vertex, i.e.
Maximum: (-1,9)
1) Substitution from definition.
2) We use
3) We are changing the order of 3 and .
4) We add 1 and 3 and we get
5) Substitution from definition (but the other way than at the beginning).
Hi! You don't actually need to graph this nor find the intersection in order to know the answer. Through the process of elimination we can rule out incorrect answers.
Firstly, we express both equations with y on the left hand side since all choices are in that form:
Knowing these, we can immediately rule out options a, c, and d since they have the wrong equations. This will leave us with option b.
You can verify if the point of intersection provided in option b is true by plugging in the values of x and y to both equations (you will find that it is indeed true).
ANSWER: b. <span>picture of coordinate plane with line y equals negative 2x minus 1 and line y equals negative 3 halves x minus 3. They intersect at 4, negative 9.</span>
Firstly, we express both equations with y on the left hand side since all choices are in that form:
Knowing these, we can immediately rule out options a, c, and d since they have the wrong equations. This will leave us with option b.
You can verify if the point of intersection provided in option b is true by plugging in the values of x and y to both equations (you will find that it is indeed true).
ANSWER: b. <span>picture of coordinate plane with line y equals negative 2x minus 1 and line y equals negative 3 halves x minus 3. They intersect at 4, negative 9.</span>