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Introduction To Vertex Form 

Basic Information of Parabolas 

  • Parabolas can open up or down

  • The zero of a parabola is where the graph crosses the x-axis

  • "Zeroes" can also be called "x-intercept(s)" or "root(s)" 

  • The axis of symmetry divides the parabola into two equal halves (If you used mirrors in grade 6 or any other grade like I did for finding the symmetry then it's basically the same but you find it without mirrors)

  • The vertex is the point where the axis of symmetry and the parabola meet

  • The vertex is also the point of the maximum or minimum value (basically the highest or lowest point of the graph)

  • The optimal value is the y co-ordinate (NOT INTERCEPT) of the vertex

  • The y-intercept is where graph crosses the y-axis

 

Transformations

Vertex Form Equation: y=a(x-h)²+k 

Vertex: (h,k)

Vertical stretch or compression by a factor of 'a' 

 

If the value of 'a' is negative then there would be a reflection on the x-axis (Parabola would open downwards)

Horizontal Translation (Movement on the x-axis)

Vertical Translation (Movement on the y-axis)

If -1<a<1, the parabola will be vertically compressed

If a>1 or a<-1, the parabola is vertically stretched

If h>0, the vertex moves to the right h units

If h<0, the vertex moves to the left h units

 

NOTE: The equation for vertex form is y=a(x-h)²+k where there is a negative sign in front of the h therefore the h value will be the opposite of the number provided

 

For example: If the equation is y=2(x-3)²+10 then the h value will not be -3 but instead it will be 3 which would make the vertex: (3,4) 

NOTE: The a value can never be 0 because that would not make the equation a parabola.

If k>0, the vertex moves up by k units

If k<0, the vertex moves down by k units

Common sense: If the k value is negative the vertex will be below zero and if the k value is positive the vertex moves above zero

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