![]() Start by separating out the non-$x$ variable onto the other side of the equation: This is similar to the check you'd do if you were solving the quadratic formula ($x= 2.6\bi x 1.2$? You should always double-check your positive and negative signs when writing out a parabola in vertex form, particularly if the vertex does not have positive $x$ and $y$ values (or for you quadrant-heads out there, if it's not in quadrant I). If you have a negative $h$ or a negative $k$, you'll need to make sure that you subtract the negative $h$ and add the negative $k$. Remember: in the vertex form equation, $h$ is subtracted and $k$ is added. Why is the vertex $(-4/3,-2)$ and not $(4/3,-2)$ (other than the graph, which makes it clear both the $x$- and $y$-coordinates of the vertex are negative)? Fortunately, based on the equation $y=3(x 4/3)^2-2$, we know the vertex of this parabola is $(-4/3,-2)$. The difference between a parabola's standard form and vertex form is that the vertex form of the equation also gives you the parabola's vertex: $(h,k)$.įor example, take a look at this fine parabola, $y=3(x 4/3)^2-2$:īased on the graph, the parabola's vertex looks to be something like (-1.5,-2), but it's hard to tell exactly where the vertex is from just the graph alone. (I think about it as if the parabola was a bowl of applesauce if there's a $ a$, I can add applesauce to the bowl if there's a $-a$, I can shake the applesauce out of the bowl.) In both forms, $y$ is the $y$-coordinate, $x$ is the $x$-coordinate, and $a$ is the constant that tells you whether the parabola is facing up ($ a$) or down ($-a$). While the standard quadratic form is $ax^2 bx c=y$, the vertex form of a quadratic equation is $\bi y=\bi a(\bi x-\bi h)^2 \bi k$. Instead, you'll want to convert your quadratic equation into vertex form. ![]() If you need to find the vertex of a parabola, however, the standard quadratic form is much less helpful. From this form, it's easy enough to find the roots of the equation (where the parabola hits the $x$-axis) by setting the equation equal to zero (or using the quadratic formula). Normally, you'll see a quadratic equation written as $ax^2 bx c$, which, when graphed, will be a parabola. The vertex form of an equation is an alternate way of writing out the equation of a parabola. Read on to learn more about the parabola vertex form and how to convert a quadratic equation from standard form to vertex form. ![]() ![]() Once you have the quadratic formula and the basics of quadratic equations down cold, it's time for the next level of your relationship with parabolas: learning about their vertex form. ![]()
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