Questions: Qual das opções a seguir é o gráfico correto de f(x) = 2x^2 + 8x - 2

Transcript text: Qual das opçōes a seguir é o gráfico correto de \[ f(x)=2 x^{2}+8 x-2 \]

Solution

Solution Steps

Step 1: Analyze the given function

The given function is f(x) = 2x² + 8x - 2. This is a quadratic function in the form ax² + bx + c, where a = 2, b = 8, and c = -2.

Step 2: Determine the properties of the parabola

Since a = 2 > 0, the parabola opens upwards. The y-intercept occurs when x = 0. f(0) = 2(0)² + 8(0) - 2 = -2. The parabola passes through the point (0, -2). The x-coordinate of the vertex is given by -b/(2a) = -8/(2*2) = -2. The y-coordinate of the vertex is f(-2) = 2(-2)² + 8(-2) - 2 = 8 - 16 - 2 = -10. So, the vertex is at (-2, -10).

Step 3: Compare with the given options

The fourth option shows a parabola that opens upwards, has a vertex at approximately (-2, -10), and a y-intercept at approximately (0, -2).

Final Answer: The fourth option is the correct graph.

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