The quadratic formula originated from the concept of completing the square. let's take ax2 + bx + c = 0.
To complete the square, solve for x.
Subtract c.
ax2 + bx = -c.
Then divide by a [notice- if there is no a value, then a=1].
x2 + bx/a = -c/a.
Add (b/2a)2 to both sides.
x2 + bx/a + b2/4a2 = -c/a + b2/4a2
Factor/Reformat.
(x + b/2a)2 = (b2-4ac) / 4a2
(x + b/2a)2 = [(b2-4ac) / 2a]2
Square-root both sides.
x + b/2a = ± √(b2-4ac) / 2a
Subtract b/2a.
x = -b/2a ± √(b2-4ac) / 2a
Combine terms.
x = [-b ± √(b2-4ac)] / 2a
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the graph for a quadratic equation ct5r
THERE ARE TWO TYPES OF QUADRATIC EQUATION1) complete quadratic equation2) incomplete quadratic equation
an equation has an equals sign.
The graph (on Cartesian coordinates) of a quadratic equation is a parabola.
A quadratic equation normally has 2 solutions and can be solved by using the quadratic equation formula.