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Minchanka [31]
2 years ago
12

Find the vertex of a quadratic function written in standard form.

Mathematics
1 answer:
Virty [35]2 years ago
3 0

Answer:

our vertex for f(x) = 3x² + 18x + 32 = (-3, 5 )

Step-by-step explanation:

let me write the standard form of a quadratic equation

a {x}^{2}  + bx + c

Now let me rewrite the original equation

3 {x}^{2}  + 18x + 32

Now we use this simple formula to find the vertex (h, k)

x = h =  -  \frac{b}{2a}  \\  =  -   \frac{18}{2(3)}  =  -  \frac{18}{6}  =  - 3 \\ h =  - 3

substitute -3 for x back into our original equation to solve for y our k value of our vertex

y = 3 ({ - 3})^{2}  + 18( - 3) + 32 \\  = 3(9) - 54 + 32 \\  = 27 + 32 - 54  \\  = 59 - 54 \\ k = 5

our vertex for f(x) = 3x² + 18x + 32 = (-3, 5 )

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