Exercise 33 Page 218

We want to draw the graph of the given quadratic function. Notice that the function is already written in vertex form, f(x)=a(x-h)^2+k, where a, h, and k are either positive or negative numbers. y=-3(x-1)^2+5 To draw the graph, we will follow four steps.

1. Identify the constants a, h, and k.
2. Plot the vertex (h,k) and draw the axis of symmetry x=h.
3. Plot any point on the curve and its reflection across the axis of symmetry.
4. Sketch the curve.Let's get started.

   Step 1

   We will first identify the constants a, h, and k. Recall that if a<0, the parabola will open downwards. Conversely, if a>0, the parabola will open upwards. Vertex Form:& y= a(x- h)^2+ k Function:& y= -3(x- 1)^2+ 5 We can see that a= -3, h= 1, and k= 5. Since a is less than 0, the parabola will open downwards.

   Step 2

   Let's now plot the vertex ( h, k) and draw the axis of symmetry x= h. Since we already know the values of h and k, we know that the vertex is ( 1, 5). Therefore, the axis of symmetry is the vertical line x= 1.

   

   Step 3

   We will now plot a point on the curve by choosing an x-value and calculating its corresponding y-value. Let's try x=0.

   y=-3(x-1)^2+5

   Substitute

   x= 0

   y=-3( 0-1)^2+5

   ▼

   Simplify right-hand side

   SubTerm

   Subtract term

   y=-3(-1)^2+5

   CalcPow

   Calculate power

   y=-3(1)+5

   MultByOne

   a * 1=a

   y=-3+5

   AddTerms

   Add terms

   y=2

   When x=0, we have y=2. As such, the point (0,2) lies on the curve. Let's plot this point and reflect it across the axis of symmetry.

   

   Note that both points have the same y-coordinate.

   Step 4

   Finally, we will sketch the parabola which passes through the three points. Remember not to use a straightedge for this!