aVertex: (- 1, - 5) Maximum or minimum point?: Minimum point
B
b - 5
Practice makes perfect
a We want to identify the vertex and decide whether it is the maximum or minimum point of the given quadratic function. Note that the formula is already expressed in graphing form, f(x)=a(x-h)^2+k, where a, h, and k are either positive or negative numbers.
f(x)=2(x+1)^2-5
It is important to note that we do not need to graph the parabola to identify the desired information. Let's compare the general formula for the graphing form to our equation.
General Formula:f(x)=& a(x- h )^2 + k
Equation:f(x)=& 2(x-( - 1))^2+(- 5)
We can see that a= 2, h= - 1, and k=- 5.
The vertex of a quadratic function written in graphing form is the point ( h,k). For this exercise, we have h= - 1 and k=- 5. Therefore, the vertex of the given equation is ( - 1,- 5).
Maximum or Minimum Value
Before we determine if the vertex is the maximum or minimum point, recall that if a>0 the parabola opens upwards. Conversely, if a<0 the parabola opens downwards.
The vertex is always the lowest or the highest point on the graph. In the given function, we have a= 2, which is greater than 0. Thus, the parabola opens upwards and the vertex represents the minimum value of the function.
b From Part A we know that the vertex is the minimum point on the graph of the given function. Thus, the y-coordinate of the vertex is the value of the function at the minimum point. Since the vertex is (- 1, - 5), the value of the function at the minimum point equals - 5.
