given: a graph
to find the zeros of the graph
Step-by-step explanation:
the zeros of the graph is nothing but the x-intercepts of the graph
so the x-intercepts of this graph are at -1, 1 and 2
so the zeros are -1, 1 and 2
the factors are: x-(-1)=x+1 ; x-1 ;x-2
so the equation becomes
f(x)=a(x+1)(x-1)(x-2)
now to get the value of a we see the x coordinate of y intercept. Here in this graph y intercept is 8 and its x coordinate is 0
f(0)= a(0+1)(0-1)(0-2)
8 = a (1)(-1)(-2)
8= a(2)
a=8/2
a=4
f(x)= 4(x+1)(x-1)(x-2)
f(x)= 4(x+1)(x²-3x+2)
f(x)=4(x³-2x²-x+2)
f(x)= 4x³-8x²-4x+8
to find y intercept we have to calculate f(0)
f(x)= 4x³-8x²-4x+8
f(0)= 4(0)³-8(0)²-4(0)+8
f(0)=0-0-0+8
f(0)=8
y intercept = 8
and even from the graph we can see that the curve is cutting the y axis at 8
the point where the curve cuts the y axis is the y intercept
final answer:
zeros of the graph: -1, 1 and 2
equation of the graph: f(x)= 4x³-8x²-4x+8
the y-intercept = 8