Answer:

Step-by-step explanation:
Step 1: Define
Difference Quotient: 
f(x) = -x² - 3x + 1
f(x + h) means that x = (x + h)
f(x) is just the normal function
Step 2: Find difference quotient
- <u>Substitute:</u>
![\frac{[-(x+h)^2-3(x+h)+1]-(-x^2-3x+1)}{h}](https://tex.z-dn.net/?f=%5Cfrac%7B%5B-%28x%2Bh%29%5E2-3%28x%2Bh%29%2B1%5D-%28-x%5E2-3x%2B1%29%7D%7Bh%7D)
- <u>Expand and Distribute:</u>
![\frac{[-(x^2+2hx+h^2)-3x-3h+1]+x^2+3x-1}{h}](https://tex.z-dn.net/?f=%5Cfrac%7B%5B-%28x%5E2%2B2hx%2Bh%5E2%29-3x-3h%2B1%5D%2Bx%5E2%2B3x-1%7D%7Bh%7D)
- <u>Distribute:</u>

- <u>Combine like terms:</u>

- <u>Factor out </u><em><u>h</u></em><u>:</u>

- <u>Simplify:</u>

Answer:
Option B. minimum is correct for the first blank
Option C. 6 is correct for second blank.
Step-by-step explanation:
In order to find the maxima or minima of a function, we have to take the first derivative and then put it equal to zero to find the critical values.
Given function is:

Taking first derivative

Now the first derivative has to be put equal to zero to find the critical value

The function has only one critical value which is 5.
Taking 2nd derivative


As the value of 2nd derivative is positive for the critical value 5, this means that the function has a minimum value at x = 5
The value can be found out by putting x=5 in the function

Hence,
<u>The function y = x 2 - 10x + 31 has a minimum value of 6</u>
Hence,
Option B. minimum is correct for the first blank
Option C. 6 is correct for second blank.
Answer:
he has 472 points now.
Step-by-step explanation:
The second leftover expression is not o(a+b). It is 6(a + b). I have attached the correct question to depict that.
Answer:
The equivalent expressions are;
8a + 2 and 6a + 6b
Step-by-step explanation:
The two leftover expressions are given as;
2(4x + 1) and 6(a + b)
In algebra, equivalent expressions are simply those expressions which when simplified, give the same resulting expression as the initial one.
Thus simply means expanding or collecting like times to make it clearer.
Now, in our question, like terms have already been collected. This means that to find an equivalent expression, we will just expand the bracket.
Thus;
2(4x + 1) will be expanded by using the 2 outside the bracket to multiply the terms inside the bracket. This gives;
8x + 2
Similarly,
6(a + b) will be expanded by using the 2 outside the bracket to multiply the terms inside the bracket. This gives;
6a + 6b
Thus;
The equivalent expressions are;
8a + 2 and 6a + 6b