Converting Quadratics: Standard Form and Vertex Form
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(0:01) 2 Forms of Quadratic Equations: The standard form: $ax^2 + bx + c$, and the vertex form, $a(x – h)^2 + k$, (where $a \neq 0$).(0:18) How to Convert Vertex Form to Standard Form?: Square the binomial, expand the brackets, and simplify. To convert the vertex form $y = 2(x – 3)^2 – 5$, first expand the squared term: $(x – 3)^2 = x^2 – 6x + 9$. Then, distribute the $2$ to get $y = 2x^2 – 12x + 18$. Finally, simplify the constants. The standard form is $y = 2x^2 – 12x + 13$.(1:13) How to Convert Standard Form to Vertex Form?: Factor out the coefficient of $x^2$, complete the square, and simplify. For example, to convert the general form $y = 3x^2 + 18x + 25$, first factor out the $3$: $y = 3(x^2 + 6x) + 25$. Next, complete the square: $y = 3[(x + 3)^2 – 9] + 25$. Finally, simplify the constants. The vertex form is $y = 3(x + 3)^2 – 2$.
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