so you would still have to guess from among the remaining three answer choices.
Knowing the vertex of a parabola can help you more easily answer questions about the minimum or
maximum value a parabolic function will reach or the x-value that results in that minimum or maximum y-
value. Say the last question was a grid-in on the No Calculator section that asked for the x-coordinate of
the vertex. You couldn’t graph it to find the vertex, so you’d have to get it into vertex form. Here are the
steps to do that.
To convert a parabola equation in the standard form to the vertex form, complete the square.- Make y = 0, and move any constants over to the left side of the equation.
- Take half of the coefficient on the x-term, square it, and add it to both sides of the equation.
- Convert the x terms and the number on the right to square form: (x − h)^2.
- Move the constant on the left back over to the right and set it equal to y again.
For the equation in the last question, you would make it 0 = x^2 – 4x − 12, then 12 = x^2 – 4x. You’d add 4
to both sides to get 16 = x^2 – 4x + 4, then convert the right side to the square form to get 16 = (x − 2)^2.
Finally, you’d move the 16 back over and set it equal to y to get y = (x − 2)^2 – 16.
The SAT will also ask questions about the equation of a circle in the xy-plane.
The equation of a circle is:(x − h)^2 + (y – k)^2 = r^2In the circle equation, the center of the circle is the point (h, k), and the radius of the circle is r.Let’s look at a question that tests the use of the circle equation.
26.Which of the following is the equation of a circle with center (2, 0) and a radius with
endpoint (5, )?
A) (x − 2)^2 + y^2 = 4
B) (x + 2)^2 + y^2 = 4
C) (x − 2)^2 + y^2 = 16
D) (x + 2)^2 + y^2 = 16