Question

How do you graph quadratics using the vertex form?

Answer 1

Hint:
In the given question, we have been asked the steps for plotting a graph of quadratic equations using vertex form. In order to graph a quadratic using vertex form, first we need to find the vertex of the given equation. Later we will find the y-intercept and the x-intercept and then plot the points we found in the above steps. In this way we can graph a quadratic equation using vertex form.

Complete step by step solution:
The vertex form of the quadratic equation is given by,
\[y=a{{\left( x-h \right)}^{2}}+k\]
Where,
\[a\] equals to the coefficient of \[{{x}^{2}}\].
‘h’ is the x-coordinate of the vertex.
‘k’ is the y-coordinate of the vertex.
Steps required to graph the quadratic equation using vertex form:
Step 1 – As the given equation we have is in vertex form, so the first step is to find the vertex. The vertex of the given equation will be at the point (h, k).
If the quadratic equation is not in vertex form, then first we need to convert the quadratic equation into vertex form by using the method of completing the square.

Step 2 – Next step is to find the y-intercept.
To find the y-intercept, we need to put x = 0 and solve the equation for the ‘y’.

Step 3 – Finding the x-intercept.
To find the x-intercept, we need to put y = 0 and solve the equation for the ‘x’. To solve for the value of ‘x’, you can use the properties of quadratic equations or you can solve by splitting the middle term or by using square root principle.

Step 4 – Plot the points of the given equation in vertex form we found in the above steps.
Therefore, these are the steps required to plot the graph of a quadratic equation using vertex form.

Note:
Students need to remember that if the given quadratic equation will not be in vertex form then you will need to first convert it into vertex form by completing the square method, so for that you will need to make a given equation a perfect square trinomial and always remember that the leading coefficient of \[{{x}^{2}}\] should be 1.