Most textbooks interpret standard form of a quadratic function to be as follows:
f(x) =
In the function f(x) =
, notice we do not have a value for "c". Just place a "0" in for the c and you have standard form.
the criteria for standard form:
1. All like terms are combined
2. Degree must drop from left to right
3. The leading coefficient cannot be equal to zero.
35,000 cm = .35 km
is your answer
It’s not hard bro you gotta lean probability it’s really easy
Answer:
The price for one cone before tax is $2.26.
Step-by-step explanation:
The tax for each cone is $.17
Ronnie buys six cones. The total tax for the cones is 6 X $.17 = $1.02
Next, we subtract the total taxes from the total price $14.58 - $1.02 = $13.56
So Ronnie owed $13.56 for the six cones BEFORE taxes. We takes this amount and divide it by six to get the cost for one cone.
$13.56 / 6 = $2.26 per cone.
Check our work
Purchase one cone for $2.26 plus $.17 cents tax = $2.43 total cost per cone.
6 cones at $2.43 each would be 6 X $2.43 = $14.58.
This matches the total bill from the story problem.
Notice that 6 is a factor of all three coefficients and thus can be factored out:
6x^2 -42x-54 => 6(x^2 - 7x - 9). x^2 - 7x - 9 does not factor so easily. Remembering that obtaining roots of a quadratic makes it easy to write out the corresponding factors, let's apply the quadratic formula to x^2 - 7x - 9:
a=1, b = -7, c = -9. Then the discriminant is b^2 - 4ac, or (-7)^2 - 4(1)(-9), or 85.
Thus, the roots are:
7 plus or minus √85 7 plus or minus 9.220
x = -------------------------------- = ------------------------------------
2 2
Let's call these roots "a" and "b." Then the factors of the quadratic x^2 - 7x - 9 are (x-a) and (x-b), or, in this case, (x-8.11) and (x+1.11).
The original quadratic has three factors: 6, (x-8.11) and (x+1.11).
