h(x)=-x^2+6x. So what is the value of h(2)

✺ Quadratic polynomials can be factored using the transformation [tex]ax^2+bx+c=a(x-x_{1})(x-x_{2} )[/tex], where [tex]x_{1}[/tex] and [tex]x_{2}[/tex] are the solutions of the quadratic equation [tex]ax^2+bx+c=0[/tex]:

[tex]-x^2+6x=0[/tex]

✺ All equations of the form [tex]ax^2+bx+c=0[/tex] can be solved using the quadratic formula:

[tex]-b=\frac{+}\\\sqrt{b^2-4ac}\\~~~~~~~~~~~~~2a[/tex]

✺ The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction:

[tex]x=\frac{\sqrt{-6\frac{+}\\\sqrt{6^2}}}{2(-1)}[/tex]

✺ Take the square root of [tex]6^2[/tex]:

[tex]x=\frac{\sqrt{-6\frac{+}\\{6}}}{2(-1)}[/tex]

✺ Multiply [tex]2[/tex] times [tex]-1[/tex]:

[tex]x=\frac{\sqrt{-6\frac{+}\\{6}}}{-2}[/tex]

✺ Now solve the equation [tex]x=\frac{\sqrt{-6\frac{+}\\{6}}}{-2}[/tex] when ± is plus. Add [tex]-6[/tex] to [tex]6[/tex]:

[tex]x=\frac{0}{-2}[/tex]

✺ Divide [tex]0[/tex] by [tex]-2[/tex]:

[tex]x=0[/tex]

-OR-

✺ Now solve the equation [tex]x=\frac{\sqrt{-6\frac{+}\\{6}}}{-2}[/tex] when ± is minus. Subtract [tex]6[/tex] from [tex]-6[/tex]:

[tex]x=\frac{-12}{-2}[/tex]

✺ Divide [tex]-12[/tex] by [tex]-2[/tex]:

[tex]x=6[/tex]

✺ Optional : Factor the original expression using [tex]ax^2+bx+c=a(x-x_{1})(x-x_{2} )[/tex]. Substitute [tex]0[/tex] for [tex]x_{1}[/tex] and [tex]6[/tex] for [tex]x_{2}[/tex]:

[tex]-x^2+6x=-x(x-6)[/tex]

✩ Answer:

✺ Factored Form: [tex]x(x-6)[/tex]

✺ Exact Form: [tex]x=6[/tex]

✺ Graph Point Form: [tex]x=(6,0)[/tex]

[tex]Hope~this~helps~and,\\Best~of~luck!\\\\~~~~~-TotallyNotTrillex[/tex]

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