# ACT Math 4.4 Coordinate Geometry

ACT Math: Coordinate Geometry Drill 4, Problem 4. Find the vertex.

ACT Math | Coordinate Geometry |

ACT Mathematics | Coordinate Geometry |

Algebra | Coordinates and Graphs |

Coordinate Geometry | Conic sections Conics |

Foreign Language | Arabic Subtitled Chinese Subtitled Korean Subtitled Spanish Subtitled |

Geometry | Coordinate Geometry |

Language | English Language |

Product Type | ACT Math |

### Transcript

y = a(x -- h) squared + k.... where the vertex is (h,k)

The k is gonna be all about how high or low the vertex of the parabola sits along the y

axis direction.

A vertex is this base point on the parabola.... its absolute bottom or top or... side thing.

So now we have this equation that they give us:

and we have to put it into standard form.

We can first subtract 1 from both sides and then factor out the 2 on the right to get

y minus 1 equals 2 times quantity x squared minus 2x.

We can now complete the square inside the parentheses...

Given x squared plus bx...we can

complete the square by adding the quantity b over 2 squared...

In this case, when we look at x squared minus 2x in the parentheses...b is negative 2..so

negative 2 divided by 2 is negative 1...and negative 1 squared is 1.

But remember, we've just completed the square in the parentheses...so we're actually adding

2 to the right side...which means we have to add 2 to the left side as well.

The right side simplifies to 2 times the quantity x minus 1 squared...and the left side simplifies

to y plus 1. We can now subtract 1 from both sides... and we see that the equation is in standard form!

We see that h is 1 and k is negative 1. So our vertex is (1, -1).

Answer's (B).