Identify the vertex of y=-1(x-4)^2+9 and tell whether it’s a minimum or maximum

Accepted Solution

Answer:Vertex = (4, 9)The vertex is the maximumStep-by-step explanation:The vertex form of a quadratic of the form [tex]y=ax^{2} +bx+c[/tex] is [tex]y = a(x - h)^{2} + k[/tex] where [tex](h,k)[/tex] are the coordinates of the vertex. Comparing the vertx form of the quadratic to our quadratic [tex]y=-1(x-4)^{2}+9[/tex], we can infer that [tex]h=4[/tex] and [tex]k=9[/tex], so its vertex is the point (4, 9).Now, in a parabola of the form [tex]y = a(x - h)^{2} + k[/tex] if [tex]a<0[/tex] the parabola open downwards and the vertex is its maximum, and if [tex]a>0[/tex] the parabola open upwards and the vertex is its minimum. We know from our parabola that [tex]a=-1[/tex]. Since [tex]-1<0[/tex], the vertex of our parabola is its maximum. We can conclude that the vertex of our parabola is (4, 9) and is its maximum.