H(x)=-5(x-1)^2+45 what is the maximum height
1 answer:
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Answer:
45
Step-by-step explanation:
The equation is that of a parabola in vertex form.
y = a(x -h)^2 +k
where 'a' is the vertical scale factor and (h, k) is the vertex.
Comparing this to the given function, you find ...
a = -5
h = 1
k = 45
The negative value of 'a' tells you the parabola opens downward, so the y-value of the vertex is the maximum value of the function: 45.
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We have that
we know that
Is the equation of a vertical parabola open down
so
the vertex is a maximum
step 1
convert the equation of the parabola in the vertex form
the vertex (h,k) is the point (0,36)
Part a) The point on the graph where the height of the tunnel is a maximum is (0,36)
Part b) The points on the graph where the height of the tunnel is zero feet is when y=0
so
for y=0
the points are (-6,0) and (6,0)
see the attached figure
we know that
Is the equation of a vertical parabola open down
so
the vertex is a maximum
step 1
convert the equation of the parabola in the vertex form
the vertex (h,k) is the point (0,36)
Part a) The point on the graph where the height of the tunnel is a maximum is (0,36)
Part b) The points on the graph where the height of the tunnel is zero feet is when y=0
so
for y=0
the points are (-6,0) and (6,0)
see the attached figure