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Remember that $a^2$ means “$2$ $a$’s multiplied together” (for example, $(-2)^2=(-2)(-2)=4$). The equation $y=x^2$ is called a quadratic equation because the highest power of a variable is $x^2$, whose exponent is $2$. In this lesson you will study this and other similar quadratic equations.
Notice that the points from the table above are plotted on the grid to the left. Click to graph the equation $y=x^2$ on the same grid.
$y=x^2+2$ is also a quadratic equation because the highest power of $x$ is $x^2$. In this section you will see how equations like $y=x^2+2$ compare to $y_1=x^2$.
Click to graph the two equations $y_1=x^2$ and $y=x^2+2$.
The equation $y=x^2+k$ is graphed on the grid to the left. Click on the slider for $k$ and move it. As you change $k$, the equation for the graph is written below the grid.
$y=(x-2)^2$ is also a quadratic equation, even though the $x^2$ term is hidden in the way the equation is written. In this section you will learn about equations like $y=(x-2)^2$.
Click to graph the two equations $y_1=x^2$ and $y=(x-2)^2$.
Click on the slider for $h$ and move it to change $h$ in the equation $y=(x-h)^2$.
Use the slider to complete the table below.
Here is the graph of the equation $y=(x-h)^2+k$. Using the sliders for $h$ and $k$, change their values and notice the effect on the graph. The equation for the parabola is shown below the grid.
Complete the table below.