Quadratic Formula

$\rhd$ The quadratic formula (16:31) The solution to three equations using the quadratic formula, and the relationship of the solutions to the graph of the function and other methods to solve the equation. The examples are: $x^2 +4x -21 = 0$ which is factorable and has two real solutions; $3x^2 +6x +10 = 0$ , which has no rational roots so cannot be factored using rational numbers — indeed it has no real solutions (the graph doesn’t intersect the $x$ -axis), so the quadratic formula is the best and easiest way to solve this problem; $-3x^2 +12x +1 = 0$ , which has two real solutions.
$\rhd$ Using the quadratic formula (rearranging) (2:21) Rewrite the equation $6x^2 + 3 = 2x - 6$ in standard form and identify $a, b$ , and $c$ .
$\rhd$ Determining the number of solutions to a quadratic using the discriminant (4:58) Example used: $x^2 +14x+49 = 0$ .
$\star$ Practice determining the number of solutions of a quadratic (including interpreting graphical information)
$\star$ Practice solving quadratic equations using the quadratic formula.
$\rhd$ Derivation of the quadratic formula (using completing the square to solve $ax^2 + bx+c = 0$

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The OpenLab at City Tech:A place to learn, work, and share

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