Subjects algebra

Axis Symmetry 921106

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1. **Problem Statement:** We are given the x-intercepts of a quadratic function's graph as points (0, -2) and (0, 6). We need to determine if the axis of symmetry is $x = -2$. 2. **Understanding the Problem:** The x-intercepts are points where the graph crosses the x-axis, so their y-values should be zero. However, the given points have x = 0 and y-values -2 and 6, which means these are actually y-intercepts, not x-intercepts. 3. **Axis of Symmetry for Quadratic Functions:** The axis of symmetry of a parabola given by $y = ax^2 + bx + c$ is the vertical line $x = -\frac{b}{2a}$. 4. **Finding the Axis of Symmetry from Intercepts:** If the x-intercepts are $x_1$ and $x_2$, the axis of symmetry is the vertical line halfway between them: $$x = \frac{x_1 + x_2}{2}$$ 5. **Given Points Analysis:** The points given are (0, -2) and (0, 6), both with $x=0$. These are not x-intercepts but y-values at $x=0$. 6. **Conclusion:** Since the x-intercepts are not given, we cannot determine the axis of symmetry from these points. The statement that the axis of symmetry is $x = -2$ is **not true** based on the given information. **Final Answer:** No, it is not true that the axis of symmetry is $x = -2$ based on the given points (0, -2) and (0, 6).