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
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?

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Answer

x=b2a\mathbf{x = -\frac{b}{2a}}

Step 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 \boxed{x = -\frac{b{2a}}}.

Step 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{(0,0)}.

Step 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{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=2x2\boxed{y = 2x^2}.

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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).

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

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.

ScanSolve AI Answer
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.