McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
Mid-Chapter Quiz
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Exercise 6 Page 132

Start by identifying a and b. Recall that for the vertex, the x-coordinate is - b2a and the y-coordinate is f(- b2a).

Vertex: ( 52,- 94)
Maximum or Minimum: Minimum

For a quadratic function f(x)=ax^2+bx+c, the y-coordinate of the vertex is the minimum value of the function when a>0. Let's identify the values of a and b in the given quadratic function. f(x)=x^2-5x+4 ⇕ f(x)= 1x^2 - 5x+4We can see above that a= 1 and b= -5. We will now use these values to find the desired information. Since a= 1 is greater than 0, the parabola will open upwards. This means it will have a minimum value, which is given by f ( - b2a ). Before we find the value of the function at this point, we need to substitute a= 1 and b= -5 in - b2a.
- b/2a
â–Ľ
Substitute values and evaluate
- -5/2( 1)
- -5/2
5/2
Now we have to calculate f( 52). To do so, we will substitute 52 for x in the given function.
f(x)=x^2-5x+4
f( 52)=( 52)^2-5( 52)+4
â–Ľ
Simplify right-hand side
f( 52)= 254-5( 52)+4
f( 52)= 254- 252+4
f( 52)=- 94
This tells us that the coordinates of the vertex are ( 52,- 94), and this is the minimum point of the given function.