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mustang
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Problem 1.
Consider the equation y=a(x-r_1)(x+r_2)
Write the equation of the axis of symmetry.
Consider the equation y=a(x-r_1)(x+r_2)
Write the equation of the axis of symmetry.
The axis of symmetry of a parabola is a line that divides the parabola into two symmetrical halves. It is a vertical line that passes through the vertex of the parabola.
To find the axis of symmetry of a parabola, you can use the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in the form y = ax^2 + bx + c. This formula gives you the x-coordinate of the vertex, which is also the x-coordinate of the axis of symmetry.
This equation represents a parabola in standard form, where a is the coefficient of the x^2 term and (r_1, 0) and (r_2, 0) are the x-intercepts of the parabola. The axis of symmetry is the line x = (r_1 + r_2)/2.
The axis of symmetry divides the parabola into two symmetrical halves, meaning that any point on one side of the axis has a mirror image on the other side. It also passes through the vertex, which is the highest or lowest point on the parabola.
No, all parabolas have an axis of symmetry. It may not be visible on the graph, but it still exists mathematically. If the parabola is in the form y = ax^2 + bx + c, the axis of symmetry is always x = -b/2a.