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If x=-1\3 is a zero of a polynomial p(x)=27xcube -axsquare -x+3 then find the value of a
1 answer:
Answer:
a = 21
Step-by-step explanation:
If x = h is a zero of a polynomial then f(h) = 0, thus
p(- ) = 27( -
)³ - a(-
) - (-
) + 3 = 0, that is
27 (- ) -
a +
+ 3 = 0
- 1 - a +
= 0 ( multiply through by 9 to clear the fractions )
- 9 - a + 30 = 0
- a + 21 = 0 ( subtract 21 from both sides )
- a = - 21 ( multiply both sides by - 1 )
a = 21
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Answer:
1) Vertex point (-1.5,-20.25)
2) axis of symmetry: x=-1.5
3) x-intercepts: (-6,0) and (3,0)
4) y-intercept: (0,18)
5) Graph in attachment.
Step-by-step explanation:
1) The given parabola has equation:
We need to complete the square.
This function is in the vertex form:
where (h,k) is the vertex, x=h is the axis of symmetry.
By comparing our equation to the general vertex form:
The vertex point is (-1.5,-20.25)
2) The axis of symmetry divides the parabola into two congruent halves.
Since this is a vertical parabola, the axis of symmetry occuring at x=h is a vertical line.
The axis of symmetry is x=-1.5
3) Y-INTERCEPT.
The y-intercept is the point where the graph cross the y-axis.
At this point, the value of x is zero.
To find the y-intercept, we substitute x=0 in the equation of the parabola and simplify.
when x=0,
The y-intercept is (0,-18).
4) X-INTERCEPT
The x-intercepts are the points where the graph touches or intersect the x-axis.
To find the x-intercept, we substitute y=0.
Add 20.25 to both sides;
Take square root.
The x-intercepts are(-6,0) and (3,0).
4) GRAPH
To graph this function, we can use transformation.
To graph the function,
We shift the parent quadratic function 1.5 units left and 20.25 units down.
See attachment for graph.
