Question

1. sketch a quadratic graph with vertex (1, 3) that increases then decreases.

Explanation:

Step1: Determine the parabola's direction

Since the graph increases then decreases, the parabola opens downwards. The vertex form of a quadratic function is \(y = a(x - h)^2 + k\), where \((h,k)\) is the vertex. Here \(h = 1,k=3\) and \(a<0\). Let's take \(a=-1\), so the function is \(y=-(x - 1)^2+3\).

Step2: Find some points

• When \(x = 0\): \(y=-(0 - 1)^2+3=-1 + 3=2\)
• When \(x = 2\): \(y=-(2 - 1)^2+3=-1 + 3=2\)
• When \(x=-1\): \(y=-(-1 - 1)^2+3=-4 + 3=-1\)
• When \(x = 3\): \(y=-(3 - 1)^2+3=-4 + 3=-1\)

Step3: Plot the points and draw the graph

Plot the vertex \((1,3)\), the points \((0,2),(2,2),(-1,-1),(3,-1)\) on the coordinate - plane. Then connect these points with a smooth curve that is a parabola opening downwards.

Answer:

Sketch a parabola opening downwards with vertex \((1,3)\) passing through points like \((0,2),(2,2),(-1,-1),(3,-1)\) (the actual sketch is done on the given coordinate - grid).