This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Step 1: Answer Question 7. For a parabola in the form y = ax^2 + bx + c, the equation of the axis of symmetry is given by: x = -(b)/(2a) The equation of the axis of symmetry of a parabola is x = -(b)/(2a). Step 2: Answer Question 8. The graph shows the parabola y = 2x^2. The vertex or turning point of a parabola in the form y = ax^2 is at the origin (0,0). This is also visible as the lowest point on the graph. The vertex or turning point of the graph is (0,0). Step 3: Answer Question 9. The axis of symmetry for the parabola y = 2x^2 is the vertical line that passes through its vertex (0,0). This line is the y-axis. The equation of the y-axis is x=0. Using the formula x = -(b)/(2a) for y = 2x^2 (where a=2, b=0, c=0): x = -(0)/(2(2)) = 0 The axis of symmetry of the graph is x=0. Step 4: Answer Question 10. The equation of the parabola is explicitly stated below the graph. The equation of the parabola is y = 2x^2.