A=9, b = 10, c =11.4, 2C = ___
2 answers:
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Answer:
quadratic
Step-by-step explanation:
The x-values are sequential, so we can look at the y-values.
Differences from one to the next are ...
-7, -1, 5, 11, 17
And the differences of these numbers are ...
6, 6, 6, 6
When <em>second</em> differences are constant, the sequence can be produced by a <em>second</em>-degree (quadratic) polynomial.
__
Here, that polynomial is ...
y = 3x² +2x -1
The regression functions of a graphing calculator can help you find the appropriate formula.
A graph of the equation shows the appropriate choice to be
C. 2
_____
If you would rather, you can look at the value of the discriminant. For the equation y = ax²+bx+c, the discriminant (d) is
d = b²-4ac
For your equation, this evaluates to
d = (-8)²-4(2)(5) = 64 -40 = 24
When the discriminant is positive, the function has two real roots (2 x-intercepts). When it is zero, there is only one x-intercept, and when it is negative, there are none (the roots are complex).
C. 2
_____
If you would rather, you can look at the value of the discriminant. For the equation y = ax²+bx+c, the discriminant (d) is
d = b²-4ac
For your equation, this evaluates to
d = (-8)²-4(2)(5) = 64 -40 = 24
When the discriminant is positive, the function has two real roots (2 x-intercepts). When it is zero, there is only one x-intercept, and when it is negative, there are none (the roots are complex).