Which relationship describes angles 1 and 2?
2 answers:
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Answer:
In general, quadratic equations have two x-intercepts. But sometimes it happens that a quadratic eqution has one x-intercept or no interepts. That's why we should fully analyze this equation:
Given the following equation: y=3x^2 + 7 + m
If y=0, then:
3x^2 + 7 + m = 0 ⇒ x^2 = (-m-7)/3
Then ±
Given that we can take the square root of a negative number, the only way this equation has two x-intercepts is if m<-7.
Summarizing:
The equation: y=3x^2 + 7 + m has two x-intercepts only if m is less than -7. If m equals -7, the equation has only one x-intercept, and finally, if m is greater than -7, the equation has NO x-intercepts.
Answer:
- Stretching the parent function vertically .
- Shifting the parent function 5 units right.
Step-by-step explanation:
<h3>The complete exercise is: " A 100 gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The function
Below are some transformations for a function :
1. If , the function is shifted "k" units up.
2. If , the function is shifted "k" units down.
3. If , the function is shifted "k" units right.
4. If , the function is shifted "k" units left.
5. If and
the function is stretched vertically by a factor of "b".
6. If and
the function is compressed vertically by a factor of "b".
The exercise gives the following parent function:
And you know that the transformed function which represents the remaining time in minutes needed to fill the tank, is:
Therefore, based on the transformations explained before you can identify that the graph of the transformed function is created by:
- Stretching the parent function vertically.
- Shifting the parent function 5 units right.