The parabola vertex is (1,5), the focus of the parabola is (1,6), and the directrix y = 4.
<h3>What is the graph of a parabolic equation?</h3>
The graph of a parabolic equation is a U-shape curve graph that is established from a quadratic equation.
From the given information:
![\mathbf{y=\dfrac{1}{4}(x-1)^2+5}](https://tex.z-dn.net/?f=%5Cmathbf%7By%3D%5Cdfrac%7B1%7D%7B4%7D%28x-1%29%5E2%2B5%7D)
The vertex of an up-down facing parabolic equation takes the form:
y = ax² + bx + c is ![\mathbf{x_v = -\dfrac{b}{2a}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bx_v%20%3D%20-%5Cdfrac%7Bb%7D%7B2a%7D%7D)
Rewriting the given equation:
![\mathbf{y = \dfrac{x^2}{4}-\dfrac{x}{2}+\dfrac{21}{4}}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%20%5Cdfrac%7Bx%5E2%7D%7B4%7D-%5Cdfrac%7Bx%7D%7B2%7D%2B%5Cdfrac%7B21%7D%7B4%7D%7D)
![\mathbf{x_v = -\dfrac{b}{2a}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bx_v%20%3D%20-%5Cdfrac%7Bb%7D%7B2a%7D%7D)
![\mathbf{x_v = -\dfrac{(-\dfrac{1}{2})}{2(\dfrac{1}{4})}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bx_v%20%3D%20-%5Cdfrac%7B%28-%5Cdfrac%7B1%7D%7B2%7D%29%7D%7B2%28%5Cdfrac%7B1%7D%7B4%7D%29%7D%7D)
![\mathbf{x_v =1}](https://tex.z-dn.net/?f=%5Cmathbf%7Bx_v%20%3D1%7D)
Replacing the value of x into the equation, y becomes:
![\mathbf{y_v = 5}](https://tex.z-dn.net/?f=%5Cmathbf%7By_v%20%3D%205%7D)
Thus, the parabola vertex is (1,5)
From the vertex, the focus of the parabola is (1,6), and the directrix y = 4.
The graphical representation of the parabola is seen in the image attached below.
Learn more about the graph of a parabolic equation here:
brainly.com/question/12896871
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Answer: $9.64
Step-by-step explanation:
The places are Tens and Millions
Answer:
1 and 2 on what? 1+2=3
Step-by-step explanation:
Oddly enough, when y=-1/3, the value of y is -1/3.
When x = -1/3, the value of y is
.. y = 3*(-1/3) -2
.. = -1 -2
.. = -3
When x = -1/3, the value of y is -3.