1. **State the problem:** Match each quadratic equation in vertex form to its verbal description by identifying the vertex $(h,k)$ and the value of $a$. 2. **Recall the vertex form:** $$y = a(x - h)^2 + k$$ - $(h,k)$ is the vertex. - $a$ determines the parabola's direction and stretch/compression. - If $a > 0$, parabola opens up; if $a < 0$, it opens down. - $|a| > 1$ means vertical stretch; $0 < |a| < 1$ means vertical compression. 3. **Analyze each equation:** **Equation 2:** $y = (x - 4)^2 + 2$ - Vertex: $(4, 2)$ - $a = 1$ (opens up, no stretch/compression) - Matches description D: Shifted right 4 units and up 2 units. **Equation 3:** $y = - (x + 2)^2 + 6$ - Rewrite vertex: $x + 2 = x - (-2)$, so vertex is $(-2, 6)$ - $a = -1$ (opens down, reflected over x-axis) - Matches description B: Reflected over the x-axis, shifted left 2 units, and up 6 units. **Equation 4:** $y = 3(x - 6)^2 - 1$ - Vertex: $(6, -1)$ - $a = 3$ (opens up, vertically stretched by factor 3) - Matches description C: Vertically stretched by a factor of 3, shifted right 6 units, and down 1 unit. **Equation 5:** $y = \frac{1}{4}(x + 1)^2 - 7$ - Vertex: $(-1, -7)$ - $a = \frac{1}{4}$ (opens up, vertically compressed by factor 1/4) - Matches description E: Vertically compressed by a factor of 1/4, shifted left 1 unit, and down 7 units. **Equation 6:** $y = -3(x - 4)^2 - 2$ - Vertex: $(4, -2)$ - $a = -3$ (opens down, reflected and vertically stretched by factor 3) - Matches description F: Reflected over the x-axis, vertically stretched by a factor of 3, shifted right 4 units, and down 2 units. **Equation 7:** $y = (x + 2)^2 - 6$ - Vertex: $(-2, -6)$ - $a = 1$ (opens up, no stretch/compression) - Matches description A: Shifted left 2 units and down 6 units. 4. **Final matches:** - 2: D - 3: B - 4: C - 5: E - 6: F - 7: A