Hello!
To find the maximum value of the function f(x) = -3(x - 10)(x - 4), the easiest way is to find the vertex using the formula: x = -b/2a.
Firstly, we need to simplify f(x).
f(x) = -3(x - 10)(x - 4)
f(x) = -3(x² - 14x + 40)
f(x) = -3x² + 42x + -120
Since the equation f(x) is now simplified to standard form, we can find the vertex.
a = -3, b = 42, and c = -120
x = -(42)/2(-3) = -42/-6 = 7
Then, we substitute 7 into the the function f(x) = -3(x - 10)(x - 4), or
f(x) = -3x² + 42x + -120, to find the y-value of the vertex.
f(x) = -3(7 - 10)(7 - 4)
f(x) = -3(-3)(4)
f(x) = 27
The vertex of f(x) is (7, 27).
Therefore, the maximum x-value for the function f(x) is 7.
Answer:
<h2><em><u>x</u></em><em><u> </u></em><em><u>=</u></em><em><u> </u></em><em><u>3</u></em><em><u> </u></em><em><u> </u></em><em><u>&</u></em><em><u> </u></em><em><u>y</u></em><em><u> </u></em><em><u>=</u></em><em><u> </u></em><em><u>5</u></em></h2>
Step-by-step explanation:
<h3>
<em><u>Given</u></em><em><u>, </u></em></h3>
(x+1, 10) = (4, 2y)
<u>First</u><u> </u><u>x</u><u> </u><u>coordinate</u><u>, </u>
x + 1 = 4
=> x = 4 - 1
=> <em>x = 3 (Ans) (i)</em>
<u>Second</u><u> </u><u>y</u><u> </u><u>coordinate</u><u>, </u>
10 = 2y

=> <em>y</em><em> </em><em>=</em><em> </em><em>5</em><em> </em><em>(</em><em>Ans</em><em>)</em><em> </em><em>(</em><em>ii</em><em>)</em>