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Find f(2) and f(a + h) when f(x) = 3x2 + 2x + 4.

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Step-by-step explanation:

[tex]f(x) = 3 {x}^{2} + 2x + 4[/tex]

[tex] \: [/tex]

[tex]f(2) = 3. {2}^{2} + 2.2 + 4[/tex]

[tex]f(2) = 3.4 + 4 + 4[/tex]

[tex]f(2) = 12 + 8[/tex]

[tex]f(2) = 20 \\ [/tex]

[tex] \: [/tex]

[tex]f(a + h) = 3 {(a + h)}^{2} + 2.(a + h) + 4[/tex]

[tex]f(a + h) = 3( {a}^{2} + 2ah + {h}^{2} ) + 2a + 2h[/tex]

[tex]f(a + h) = 3 {a}^{2} + 6ah + 3 {h}^{2} + 2a + 2h + 4[/tex]

[tex]f(a + h) = 3 {a}^{2} + 3 {h}^{2} + 6ah + 2a + 2h + 4[/tex]

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