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1. Determine the vertex and the domain and range of the function 𝑓(𝑥) = 4𝑥 − 𝑋 ꓥ2

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Answer to a math question 1. Determine the vertex and the domain and range of the function 𝑓(𝑥) = 4𝑥 − 𝑋 ꓥ2

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Neal
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104 Answers
1. Encuentra el vértice de la parábola. La función dada es de la forma ax^2 + bx + c . Aquí, a = -1 y b = 4 . El vértice V(x, y) se encuentra usando la fórmula:
x = -\frac{b}{2a} = -\frac{4}{2(-1)} = 2
Sustituye x = 2 en la función para encontrar la coordenada y :
f(2) = 4(2) - (2)^2 = 8 - 4 = 4
Por lo tanto, el vértice es V(2, 4) .

2. El dominio de una función cuadrática es siempre (-\infty, \infty) .

3. Como la parábola abre hacia abajo (porque a = -1 es negativo), el valor máximo es el valor en el vértice, que es 4. Por lo tanto, el recorrido es (-\infty, 4] .

Respuesta incuye:
\text{Vértice: } V(2, 4)
\text{Dominio: } (-\infty, \infty)
\text{Recorrido: } (-\infty, 4]

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