Question

1. draw the parabola for the set of analysis given below. 5 marks

draw the axis of symmetry and state its equation | $x = 3$
draw and state the zeroes (x - intercepts) | $x = 2$, $x = 4$
draw and state the y - intercept | $y = 8$
state the direction of opening of the parabola | up
draw and state the vertex as an (x, y) point | $(3, -1)$

Explanation:

Step1: Plot the vertex

Mark the point $(3, -1)$ on the grid.

Step2: Draw axis of symmetry

Draw a vertical line through $x=3$.

Step3: Plot intercepts

Mark x-intercepts $(2, 0)$ and $(4, 0)$; mark y-intercept $(0, 8)$.

Step4: Sketch the parabola

Connect points smoothly, opening upward, symmetric over $x=3$.

Answer:

1. Axis of symmetry: Vertical line $x=3$ drawn through the vertex.
2. X-intercepts: Points $(2, 0)$ and $(4, 0)$ plotted.
3. Y-intercept: Point $(0, 8)$ plotted.
4. Direction of opening: Upward (parabola curves upward from vertex).
5. Vertex: Point $(3, -1)$ plotted, forming the lowest point of the upward-opening parabola symmetric over $x=3$.

(Visual: A smooth upward-opening parabola with vertex at $(3,-1)$, crossing the x-axis at $(2,0)$ and $(4,0)$, crossing the y-axis at $(0,8)$, and symmetric about the vertical line $x=3$.)