Question

How do I graph the quadratic equation \[y=\dfrac{1}{4}{{\left( x-2 \right)}^{2}}+4\]?

Answer 1

Hint: We need to draw the graph of \[y=\dfrac{1}{4}{{\left( x-2 \right)}^{2}}+4\]. As this is a quadratic equation, its graph will be a parabola. To plot a parabola, we will need the vertex of the parabola, and the type of quadratic. Whether it is opening upward or opening downward. A quadratic is opening upward if the coefficient of the square term is positive, otherwise it is opening downward. We can check the coefficient by expanding the equation.

Complete step by step solution:
We are asked to plot the graph of \[y=\dfrac{1}{4}{{\left( x-2 \right)}^{2}}+4\]. The degree of this equation is two, thus it is a quadratic equation. We know that the graph of quadratic is parabola. To plot a parabola, we should know the vertex and type of parabola.
The equation \[y=\dfrac{1}{4}{{\left( x-2 \right)}^{2}}+4\] represents the parabola. Let us first find the vertex of the parabola. Since the quadratic equation is in vertex for \[y=a{{\left( x-h \right)}^{2}}+k\], whose vertex is at point $\left( h,k \right)$.
Therefore, comparing the given equation with the vertex form of the equation, we get the vertex as (2, 4).
The equation is \[y=\dfrac{1}{4}{{\left( x-2 \right)}^{2}}+4\], as we can see that the equation of the square term for this equation will be positive, the parabola will be opening upward.
Using this, we can plot the graph of quadratic equation as follows:

Note: To Solve this question, we should know the vertex form of the parabola which is expressed as \[y=a{{\left( x-h \right)}^{2}}+k\], and that its vertex is at $\left( h,k \right)$. For a general quadratic equation also, we should find the vertex and the type of parabola to plot the graph.