Which of the following graphs is described by the function given below?
y = 2x^2 + 8x + 3

Option A

Step-by-step explanation:

Equation of the given quadratic function is,

y = 2x² + 8x + 3

y = 2(x² + 4x) + 3

  = 2(x² + 4x + 4 - 4) + 3

  = 2(x + 2)² - 8 + 3

  = 2(x + 2)² - 5

By comparing this equation with the equation of a quadratic function in vertex form,

y = a(x - h)² + k

Here (h, k) is the vertex of the parabola

Vertex of the given equation will be (-2, -5) and coefficient 'a' is positive (a > 0)

Therefore, vertex will lie in the 3rd quadrant and the parabola will open upwards.

Option (A). Graph A will be the answer.

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