What is the equation, in standard form, of a parabola that models the values in the table? x~ -1 0 2
1 answer:
<h2>Steps</h2>
- Standard Form Equation: f(x) = ax² + bx + c
So firstly, since (0,5) is one of our values we can plug it into the standard form equation to solve for the c variable (since 0 will cancel out the a and b variable):
Now we know that the value of c is 5. Next, plug in (-1,12) into the standard form equation and simplify (remember to also plug in 5 for the c variable):
Next, plug (2,15) into the standard form equation and simplify:
Now, with our last two simplified equations we will create a system of equations:
Now, I will be using the elimination method with this system. With the system, add up the equations together and you will get:
From here, we can solve for the a variable. With it, just divide both sides by 3:
Now that we know the value of a, plug it into either equation to solve for the b variable:
Putting all of our obtained values together, your final answer is:
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To calculate minimum value, do -b/2a to get the x-value, and plug it in to get the y-value:
-6/8 = -3/4
So the minimum value of g(x) is -81/4
This shows that g(x) has a lesser minimum value than f(x)
-6/8 = -3/4
So the minimum value of g(x) is -81/4
This shows that g(x) has a lesser minimum value than f(x)
Hi there! The answer is D.
The parent function is the simplest form of a function. We can distinguish a variety of parent functions like linear, exponential, square root, absolute, logarithmic, quadratic, cubic, rational or constant (trigonometric functions excluded).
Now we can have a look at the function.
The thing that is the most important in this function is the square root, because this mainly decides the way the function looks. Therefore, the parent function is the simplest form of a square root function, which is the following:
Therefore the answer is D.
~ Hope this helps you!
The parent function is the simplest form of a function. We can distinguish a variety of parent functions like linear, exponential, square root, absolute, logarithmic, quadratic, cubic, rational or constant (trigonometric functions excluded).
Now we can have a look at the function.
The thing that is the most important in this function is the square root, because this mainly decides the way the function looks. Therefore, the parent function is the simplest form of a square root function, which is the following:
Therefore the answer is D.
~ Hope this helps you!