Exercise 11 Page 61

We want to draw the graph of the given quadratic function. To do so, we will rewrite it in vertex form, f(x)=a(x-h)^2+k, where a, h, and k are either positive or negative numbers. y=-1/4(x+2)^2+1 ⇕ y=-1/4(x-(- 2))^2+1 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:& f(x)= a(x- h)^2+ k Function:& y= -1/4(x-( - 2))^2+ 1 We can see that a= - 14, h= - 2, and k= 1. 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 ( - 2, 1). Therefore, the axis of symmetry is the vertical line x= - 2.

   

   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=3.
   y=-1/4(x+2)^2+1

   Substitute

   x= 3

   y=-1/4( 3+2)^2+1

   ▼

   Simplify right-hand side

   AddTerms

   Add terms

   y=-1/4(5)^2+1

   CalcPow

   Calculate power

   y=-1/4(25)+1

   MoveRightFacToNum

   a/c* b = a* b/c

   y=-25/4+1

   CalcQuot

   Calculate quotient

   y=-6.25+1

   SubTerm

   Subtract term

   y=- 5.25
   When x=3, we have y=5.25. Thus, the point (3,5.25) 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!