Question

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Answer 1

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:

$\mathbf{y=\dfrac{1}{4}(x-1)^2+5}$

The vertex of an up-down facing parabolic equation takes the form:

y = ax² + bx + c  is $\mathbf{x_v = -\dfrac{b}{2a}}$

Rewriting the given equation:

$\mathbf{y = \dfrac{x^2}{4}-\dfrac{x}{2}+\dfrac{21}{4}}$

$\mathbf{x_v = -\dfrac{b}{2a}}$

$\mathbf{x_v = -\dfrac{(-\dfrac{1}{2})}{2(\dfrac{1}{4})}}$

$\mathbf{x_v =1}$

Replacing the value of x into the equation, y becomes:

$\mathbf{y_v = 5}$

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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