1. **Problem:** Find the equation of the axis of symmetry and the coordinates of the vertex of the parabola. 2. **Formula and rules:** - The axis of symmetry of a parabola in the form $y = ax^2 + bx + c$ is the vertical line $x = -\frac{b}{2a}$. - The vertex is the point $(x, y)$ where $x$ is the axis of symmetry and $y$ is the minimum or maximum value of the parabola. 3. **Given information:** - The parabola opens upward and is centered at $x=3$. - The vertex is at $(3, -4)$. 4. **Axis of symmetry:** - Since the parabola is symmetric about $x=3$, the axis of symmetry is $x=3$. 5. **Vertex coordinates:** - The vertex is at $(3, -4)$. 6. **Answer choice:** - The correct option is (1) $y=3$ and $(3, -4)$ is incorrect because axis of symmetry is vertical line $x=3$, not $y=3$. - Option (3) $y=-3$ and $(3, -4)$ is incorrect for the same reason. - Option (4) $y=-3$ and $(4, -3)$ is incorrect because vertex coordinates do not match. - The correct axis of symmetry is $x=3$ and vertex $(3, -4)$, which matches option (1) if corrected to $x=3$. **Final answer:** Axis of symmetry: $x=3$, Vertex: $(3, -4)$. --- 1. **Problem:** Find the product of $\sqrt{60}$ and $\sqrt{15}$. 2. **Formula:** $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$. 3. **Calculation:** $$\sqrt{60} \times \sqrt{15} = \sqrt{60 \times 15} = \sqrt{900}$$ 4. **Simplify:** $$\sqrt{900} = 30$$ 5. **Answer:** The product is 30, which is an integer. --- 1. **Problem:** Find the $x$ value where $f(x) = 2x + 5$ and $g(x) = \frac{1}{2}x - 7$ intersect. 2. **Set equal:** $$2x + 5 = \frac{1}{2}x - 7$$ 3. **Solve for $x$:** $$2x + 5 = \frac{1}{2}x - 7$$ $$2x - \frac{1}{2}x = -7 - 5$$ $$\frac{4}{2}x - \frac{1}{2}x = -12$$ $$\frac{3}{2}x = -12$$ $$x = \frac{-12}{\frac{3}{2}} = -12 \times \frac{2}{3} = -8$$ 4. **Answer:** $x = -8$ is not among the options, so re-check the problem or options. --- 1. **Problem:** Evaluate $x^0$. 2. **Rule:** For any $x \neq 0$, $x^0 = 1$. 3. **Answer:** $1$. --- 1. **Problem:** Simplify $3 - 5i + 4 + 8i$. 2. **Combine like terms:** - Real parts: $3 + 4 = 7$ - Imaginary parts: $-5i + 8i = 3i$ 3. **Answer:** $7 + 3i$.