The parabola vertex is (1,5), the focus of the parabola is (1,6), and the directrix y = 4.
What is the graph of a parabolic equation?
The graph of a parabolic equation is a U-shape curve graph that is established from a quadratic equation.
From the given information:
[tex]\mathbf{y=\dfrac{1}{4}(x-1)^2+5}[/tex]
The vertex of an up-down facing parabolic equation takes the form:
y = ax² + bx + c is [tex]\mathbf{x_v = -\dfrac{b}{2a}}[/tex]
Rewriting the given equation:
[tex]\mathbf{y = \dfrac{x^2}{4}-\dfrac{x}{2}+\dfrac{21}{4}}[/tex]
[tex]\mathbf{x_v = -\dfrac{b}{2a}}[/tex]
[tex]\mathbf{x_v = -\dfrac{(-\dfrac{1}{2})}{2(\dfrac{1}{4})}}[/tex]
[tex]\mathbf{x_v =1}[/tex]
Replacing the value of x into the equation, y becomes:
[tex]\mathbf{y_v = 5}[/tex]
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:
https://brainly.com/question/12896871
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