Vertex Form of a Quadratic Equation

Key Questions

  • How do you graph quadratic equations written in vertex form?

    Answer:

    #" "#
    Please read the explanation.

    Explanation:

    #" "#
    Quadratic Equations in Vertex Form have a general form:

    #color(red)(y=f(x)=a(x-h)^2+k#, where

    #color(red)((h,k)# is the #color(blue)("Vertex"#

    Let us consider a quadratic equation in Vertex Form:

    #color(blue)(y=f(x)=(x-3)^2+8#, where

    #color(green)(a=1; h=3; k=8#

    Hence, #color(blue)("Vertex "= (3, 8)#

    To find the y-intercept, set #color(red)(x=0#

    #y=(0-3)^2+8#

    #y=9+8#

    #y= 17#

    Hence, the y-intercept: #color(blue)((0, 17)#

    We can use a table of values to draw the graph:

    enter image source here

    Use the table with two columns #color(red)(x and y# to draw the graph as shown below:

    enter image source here

    The Parent Graph of #color(red)(y=x^2# can also be seen for comparison, to better understand transformation.

    Also note that,

    Axis of Symmetry is #color(red)(x=h#

    #rArr x= 3#

    We can verify this from the graph below:

    enter image source here

    Hope it helps.

    Sridhar V. · 1 · Jul 25 2018
  • How do you find the vertex form of a quadratic equation?

    Since the equation is:

    #y=x^2+bx+c#

    the vertex is #V(-b/(2a),-Delta/(4a))#,

    or, found the #x_v=-b/(2a)# you can substitue it in the equation of the parabola at the place of #x#, finding the #y_v#.

    Massimiliano · 1 · Feb 20 2015
  • What is the Vertex Form of a Quadratic Equation?

    Vertex Form

    #y=a(x-h)^2+k#,

    where #(h,k)# is the vertex.

    I hope that this was helpful.

    Wataru · 1 · Nov 6 2014

Questions

Quadratic Equations and Functions