Question

1. complete the analysis for the following parabola. (5 marks)

draw the axis of symmetry and state its equation
draw and state the zeros (x-intercepts)
draw and state the y-intercept
state the direction of opening of the parabola
draw and state the vertex as an (x, y) point

Explanation:

Step1: Identify axis of symmetry

The axis of symmetry is the vertical line through the vertex, given by $x = h$ where $(h,k)$ is the vertex. From the graph, the vertex's x-coordinate is 2.
$x=2$

Step2: Find x-intercepts (zeroes)

Locate where the parabola crosses the x-axis. The graph crosses $x=-1$ and $x=5$.
$(-1,0), (5,0)$

Step3: Find y-intercept

Locate where the parabola crosses the y-axis. The graph crosses the y-axis at $y=5$.
$(0,5)$

Step4: Determine opening direction

The parabola curves downward, so it opens downward.
Downward

Step5: Identify vertex

The vertex is the highest point of the downward-opening parabola, at $(2,5)$.
$(2,5)$

Answer:

• Axis of symmetry: $x=2$
• Zeroes (x-intercepts): $(-1, 0)$ and $(5, 0)$
• y-intercept: $(0, 5)$
• Direction of opening: Downward
• Vertex: $(2, 5)$