## Topic 5 Review 21. **Given** \( y = (x + 3)^2 - 1 \). a. **What is the axis of symmetry?** \( x = -3 \) b. **The vertex:** \((-3, -1)\) c. **Open up or down?** Up d. **Max or min (circle) value:** Min: \(-1\) e. **What are the x-intercepts?** \((-2, 0)\), \((-4, 0)\) f. **The range:** \( y \geq -1 \) g. **Graph:** - The graph depicts a parabola opening upwards with its vertex at \((-3, -1)\). - The x-intercepts are at \((-2, 0)\) and \((-4, 0)\). - The parabola is symmetric about the vertical line \(x = -3\).2. **Consider the parabola with equation \( y = 2x^2 - 8x - 5 \).** - h. **What is the equation in vertex form?** - The graph shows a different parabola. The vertex is not labeled, but the graph indicates it passes through prominent points such as \((-2, 4)\) with notable curvature. - This parabola likely has a different axis of symmetry and vertex due to its unique equation. Additional calculations might be needed for precise details.

The given function .The aim is to find the axis of symmetry, vertex, open or down, maximum or minimum, -intercepts, range, and sketch its graph.Note: Since you have posted multiple questions, we will provide the solution only to the first question as per our Q&A guidelines. Please repost the remaining questions separately.The general form of the quadratic equation .The given equation .Compared to the general equation, the values are .(a) Axis of symmetry:The axis of symmetry is .Thus the axis of symmetry is .(b)The vertex is .Thus the vertex is .(c)If , then the parabola opens downward and if , the parabola opens upward.Here , thus the parabola opens up.(d)If , the parabola has a maximum value of .If , the parabola has a minimum value of .Thus the given parabola has a minimum value of .(e) -intercepts:Put and solve for .The -intercepts are and .(f)The parabola opens up, thus the range is .Thus the range is .The graph of the parabola .(a) Axis of symmetry: .(b) Vertex: .(c) Open up.(d) Minimum value: .(e) -intercepts: and .(f) Graph of the function is sketched.