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The equation of the axis of symmetry of a parabola is . What is the vertex or turning point of the graph? What is the axis of symmetry of the graph? What is the equation of the parabola?

Mathematics

ScanSolve AI Answer

Graph of y = 2x²

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Key points of y = 2x²
Pointxy
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Step-by-step solution

4 steps
  1. Answer Question 7.

    For a parabola in the form y=ax2+bx+cy = ax^2 + bx + c, the equation of the axis of symmetry is given by:

    x=−b2ax = -\frac{b}{2a}

    The equation of the axis of symmetry of a parabola is x=−b2a\boxed{\mathbf{x = -\frac{b}{2a}}}.

  2. Answer Question 8.

    The graph shows the parabola y=2x2y = 2x^2. The vertex or turning point of a parabola in the form y=ax2y = ax^2 is at the origin (0,0)(0,0). This is also visible as the lowest point on the graph.
    The vertex or turning point of the graph is (0,0)\boxed{\mathbf{(0,0)}}.

  3. Answer Question 9.

    The axis of symmetry for the parabola y=2x2y = 2x^2 is the vertical line that passes through its vertex (0,0)(0,0). This line is the y-axis.
    The equation of the y-axis is x=0x=0.
    Using the formula x=−b2ax = -\frac{b}{2a} for y=2x2y = 2x^2 (where a=2a=2, b=0b=0, c=0c=0):

    x=−02(2)=0x = -\frac{0}{2(2)} = 0

    The axis of symmetry of the graph is x=0\boxed{\mathbf{x=0}}.

  4. Answer Question 10.

    The equation of the parabola is explicitly stated below the graph.
    The equation of the parabola is y=2x2\boxed{\mathbf{y = 2x^2}}.

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