This is a formula-based topic that the SAT will test you on.

The standard form of a parabola is

$$y={ax}^2+bx+c$$

The **vertex form** of a parabola is

$$boldsymbol yboldsymbol=boldsymbol aboldsymbol(boldsymbol xboldsymbol-boldsymbol hboldsymbol)^{mathbf2}boldsymbol+boldsymbol k$$

Just like in the standard form, *a* controls whether the parabola opens up (*a *is positive) or down (*a* is negative).

*h* and *k* are the coordinates for the vertex of the equation. This might be written as (*h,k*).

An example:

What is the vertex of the following parabola: (y=3(x+3)^2-4) ?

**Strategy****:**

**Know the formula and fully understand all components of it.**

Another example:

Which of the following is true about the parabola with the equation (y=a{(x-b)}^2+c) where (a>0)?

A) The vertex is ((b,c)) and the graph opens upward.

B) The vertex is ((b,c)) and the graph opens downward.

C) The vertex is ((-b,c)) and the graph opens upward.

D) The vertex is ((-b,c)) and the graph opens downward.

This question is asking if you understand how the vertex form of a parabola equation works.

Since *a* is positive, we know the parabola opens upward, so can immediately rule out B and D. Because the standard formula is (*x *– *h*), and here we have (*x* – *b*), we know it is just *b* for our *x* coordinate, giving us answer **A**. If it has been (*x*+ *b*), then we would have selected answer C.

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