[Video] Q12: The function f is defined by f(x) = (x+3)(x+1). the graph of f in the xy-plane is a parabola. which of the following intervals contains the x-coordinate of the vertex of the graph of f ?

Explanation for Question 12 From the Math (No Calc) Section on the Official Sat Practice Test 7

Question 12 says the function F is defined by F of X is equal 2 to X plus three times X plus one, 3 the graph of the F and the X Y plane is a parabola, 4 which of the following intervals contains the X coordinate of the vertex, 5 the graph of F. So the first thing that I know here is 6 two points. I know that the point negative three, 7 zero is on this graph and negative one, 8 zero is on this graph. And that's just because the factors are X 9 plus three and X plus one, 10 which means that if you plug in these X values, 11 you'll get zero as a white value because parabolas are symmetrical. 12 The vertex is always just the midpoint of any two points that have the 13 same Y value. Since these two points both have the same Y value of 14 zero, whatever the midpoint of the X values are, 15 is just the X coordinate of the, 16 of the, uh, vertex. So, 17 because I know that negative three and negative one are at the same, 18 Y value the coordinate in the middle of those two negative two must be 19 the X value of the vertex. 20 And the only range that actually fits negative two is B. 21 So that means that that must be the correct.