HELLO ANY MATH EXPERTS HERE THEN PLEASE ANSWER THIS !!!
2 answers:
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Answer:
The answer is "(27,3]"
Step-by-step explanation:
Please find the complete question in the attached file.
This is an interesting question. Wish there were more questions of this kind.
This question helps us recognize the use of the vertex form of a quadratic expression/function.
The vertex form is in the form
The extreme value of the function occurs when x=h, i.e. when the first term vanishes, which leaves the value of the function equal to k. I.e. the vertex of the function is at (h,k).
For example, when
f(x)=5(x-4)^2+7
at x=4, f(4)=5(4-4)^2+7=5(0)+7=7,
in other words, f(x) is at its minimum when x=4, with a value of 7,
even simpler, the vertex of the function is at (4,7).
How do we know if it is a maximum or minimum?
If the first parameter "a" is positive, then at any other value than x=h, the function has a greater value than the vertex, hence a>0 => minimum.
Similarly, if the first parameter "a" is negative, then whenever x does not equal h, the value of the function is smaller, hence a<0 => maximum.
For example, with f(x)=5(x-4)^2+7, a=+5 >0, so (4,7) is a minimum.
Check: f(0)=5(0-4)^2+7=16+7=23 > 7, or (0,23) verifies that (4,7) is a minimum.
For given situations A, B, C, & D, we see that only one function is in the vertex form, i.e. y=a(x-h)+k, namely situation B
B. y=-3(x-2)^2+5, where a=-3, h=2 and k=5.
This means that the function has a maximum at the vertex (2,5). It has a maximum because a=-3 < 0, as discussed above.
Oh yes, enjoy the rest of April Fools Day! lol
This question helps us recognize the use of the vertex form of a quadratic expression/function.
The vertex form is in the form
The extreme value of the function occurs when x=h, i.e. when the first term vanishes, which leaves the value of the function equal to k. I.e. the vertex of the function is at (h,k).
For example, when
f(x)=5(x-4)^2+7
at x=4, f(4)=5(4-4)^2+7=5(0)+7=7,
in other words, f(x) is at its minimum when x=4, with a value of 7,
even simpler, the vertex of the function is at (4,7).
How do we know if it is a maximum or minimum?
If the first parameter "a" is positive, then at any other value than x=h, the function has a greater value than the vertex, hence a>0 => minimum.
Similarly, if the first parameter "a" is negative, then whenever x does not equal h, the value of the function is smaller, hence a<0 => maximum.
For example, with f(x)=5(x-4)^2+7, a=+5 >0, so (4,7) is a minimum.
Check: f(0)=5(0-4)^2+7=16+7=23 > 7, or (0,23) verifies that (4,7) is a minimum.
For given situations A, B, C, & D, we see that only one function is in the vertex form, i.e. y=a(x-h)+k, namely situation B
B. y=-3(x-2)^2+5, where a=-3, h=2 and k=5.
This means that the function has a maximum at the vertex (2,5). It has a maximum because a=-3 < 0, as discussed above.
Oh yes, enjoy the rest of April Fools Day! lol