Resources for Quadratic Equations

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An equation in which the highest power of the variable is 2 is called a quadratic equation, for example, \(y = 2{x^2} + 5\).
The graph of \(y = {x^2}\) is of parabola's shape and is concave up with turning point or vertex as \((0,0)\).
The graph of \(y = {x^2}\) is of parabola's shape and is concave down with turning point or vertex as \((0,0)\).
The graph of \(y = a{x^2}\) where \(a\) is a constant (number), the size of \(a\) affects whether the parabola is 'wide' or 'narrow'. For example,
\(y = \frac{{{x^2}}}{2},y =  4{x^2}\).
The graph of \(y = a{x^2}+c\) where \(a\) and \(c\) are constants, the effect of \(c\) is to move the parabola up or down from the origin.
Example 1
a. Graph \(y={x^2},y={x^2}+3,y={x^2}2 and y={x^2}5\) on the same set of axes.
b. Compare each parabola with the parabola \(y={x^2}\)
\(y={x^2}+3\) is \(y={x^2}\) shifted up \(3 units\)
\(y={x^2}2\) is \(y={x^2}\) turned upside down and shifted down \(2 units\)
\(y={x^2}5\) is \(y={x^2}\) turned upside down and shifted down \(5 units\)
c. What is the vertex of each parabola and is each parabola concave up or concave down?
\(y={x^2}\) has vertex \((0,0)\) and is concave up.
\(y={x^2}+3\) has vertex \((0,3)\) and is concave up.
\(y={x^2}2\) has vertex \((0,2)\) and is concave down.
\(y={x^2}5\) has vertex \((0,5)\) and is concave down.