![]() ![]() There are two options: completing the square or using the other formula. For most people this only works if the factors are whole numbers. If you can spot how to factorise this then that would be the quicker method. Initial step is to set #y=0# It has to be 0 for the graph to cross the axis as x-axis is at #y=0# Sometimes determining these can take a bit or work. ![]() Some people state that there is still two but they are the same as each other. Note that the vertex is the point of maximum or minimum.Ģ of these x-intercepts exist if the graph crosses the x-axisġ of these exists if the x-axis is tangential to the vertex. This takes on the value of #c# in #y=ax^2+bx+c# This uses the beginnings of completing the square. ![]() #color(blue)("Axis of symmetry - a sort of cheat method")# Plot the vertex and x-intercepts and sketch a parabola through the points. Substitute #0# for #y# and use the quadratic formula to find the roots and the x-intercepts. Vertex: #(9/2,-55/2)#larr# minimum point of the parabola For example, #color(magenta)3/color(magenta)3=1# Recall that any whole number, #n#, is understood to have a denominator of #1#. Multiply fractions without a denominator of #4# by a multiplier equal to #1# that will produce an equivalent fraction with a denominator of #4#. To determine the #y#-value, substitute #9/2# for #x# in the equation and solve for #y#.Īll terms must have a common denominator of #4#. If #a<0#, the vertex is the maximum point and the parabola will open downward. If #a>0#, the vertex is the minimum point and the parabola will open upward. Vertex: the maximum or minimum point of the parabola. #x=9/2#larr# axis of symmetry and #x#-value for the vertex The variable for the line is #x=(-b)/(2a)#. The y-intercept is helpful, also.Īxis of Symmetry: vertical line #(x,+-oo)# that divides the parabola into two equal halves. To graph a quadratic function, you need to have at least the vertex and x-intercepts. #y=2x^2-18x+13# is a quadratic equation in standard form: ![]()
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