Print this Page
9.4 – Parabolas
Key Terms
 Standard Form – An equation of a parabola in the forms:
 (opens up or down)
 (opens left or right)
 Vertex Form – An equation of a parabola in the form:
 (opens up or down)
 (opens left or right)
 h = horizontal
 v = vertical
Notes
Parabolas 
 Four kinds of parabolas
 Opening left
 Opening right
 Opening up
 Opening down

Vertex of a Parabola 
 The vertex of a parabola is the point on the parabola where the curve makes the sharpest turn.
 It’s where the curve changes directions.

Coefficients 
 If the coefficient is close to zero, then the parabola is wide and shallow.
 If the coefficient is far away from zero (a large positive number or a negative number much less than zero), then the parabola is steep and narrow.
 The coefficient can’t be zero. If it’s zero, then it’s not a parabola. It’s a line.
 The closer the coefficient gets to zero, the closer the parabola gets to being a line.

Parabolas that Open Up or Down (Centered at the Origin) 
Parabolas that Open Left or Right (Centered at the Origin) 
 Coefficient of
 If the coefficient of is positive, then the parabola opens upward.
 If the coefficient of is negative, then the parabola opens downward.

 Coefficient of
 When the coefficient of is positive, the parabola opens to the right.
 When the coefficient of is negative, the parabola opens to the left.

 Equation:
 (0, 0) = Vertex of the parabola
 (x, y) = Any point on the parabola
 a = A nonzero number

 Equation:
 (0, 0) = Vertex of the parabola
 (x, y) = Any point on the parabola
 a = A nonzero number

Parabolas Not Centered at the Origin 
 Vertex – for parabolas, (h, v) is the vertex because there is no center (like in a circle).
 How to Shift a Parabola’s Vertex from the Origin (0, 0) to (h, v)
 Subtract h from the xterm and v from the yterm.
 Isolate the variable that is not squared on one side of the equation.

Parabolas that Open Up or Down (Not Centered at the Origin) 
Parabolas that Open Left or Right (Not Centered at the Origin) 
 Equation:

 Equation:

 Coefficient
 Find the yvalue of the point 1 unit to the right of the vertex.
 Subtract the yvalue of the point at the vertex from the value you found in step 1.
 Vertex: (h, v)
 1 Unit to the Right: (h+1, v_1)
 Finding a: new yvalue minus original yvalue:

 Coefficient
 Find the xvalue of the point 1 unit above the vertex of the parabola.
 Subtract the xvalue of the point at the vertex from the value you found in step 1.
 Vertex: (h, v)
 1 Unit Above: (h_1, v+1)
 Finding a: new xvalue minus original xvalue:

Important!
Practice (Apex Study 9.4)
 Try practice problems on Pgs 10, 11, 24, 30
 Mandatory: write and answer problems on Pgs 12, 25, 31
 3 Quizzes
Permanent link to this article: http://newvillagegirlsacademy.org/math/?page_id=4384