Answer:
An example of a quadratic equation is:
Step-by-step explanation:
This answer follows the standard form for a quadratic equation:
To solve this equation you do the following:
x^2 + 5x + 6 =0
The factors that can be added to get *5* and multiplied to get *6* are 3 & 2.
Therefore the new equation would be:
x^2 +3x + 2x + 6 = 0
<em>group the terms</em>: (x^2 +3x) (+2x + 6) = 0
<em>factorize</em><em>:</em><em> </em>x (x + 3) 2 (x + 3) = 0
<em>therefore</em><em>:</em><em> </em><em>(</em><em>x</em><em> </em><em>+</em><em> </em><em>2</em><em>)</em><em> </em><em>(</em><em>x</em><em> </em><em>+</em><em> </em><em>3</em><em>)</em><em> </em><em>=</em><em>0</em>
<em>x</em><em> </em><em>=</em><em> </em><em>-1</em><em> </em><em> </em><em>x</em><em> </em><em>=</em><em>-3</em>
Answer:
f(x) = -4x²+24x -28
Step-by-step explanation:
The given zeros are a sum and a difference. You can use the special factoring of the product of a sum and difference to simplify the product of the factors of the quadratic. Each zero 'p' corresponds to a factor (x -p):
f(x) = a(x -(3 +√2))(x -(3 -√2)) = a((x -3)² -(√2)²) = a((x -3)² -2)
We can find the leading coefficient 'a' from the given point:
f(1) = -8 = a((1 -3)² -2) = 2a
a = -8/2 = -4
Then the function can be written as ...
f(x) = -4((x -3)² -2) = -4(x² -6x +9 -2)
f(x) = -4x²+24x -28
You have a function
.
Since the range of the function
is
you have that
.
Answer: The range of given function is [0,3] and the correct choice is C.
Answer:
28.26
Step-by-step explanation:
For problems like these, it's very helpful for looking at key words. 'How many more' suggests that one value is greater than the other by a certain amount, which means subtraction. Let's do the same for this equation.
If 165 is m greater than 130, then this means .
This will also mean that m is 130 less than 165. To solve this, isolate the variable and subtract 130 from both sides:
We will end up with m = $35. To prove this, plug 35 into the m value as shown below:
, so the answer is $35 more is needed.