Attempt following question by selecting a choice to answer.
f
For what values of
b and
c, the function
y = 8x2 + bx + c will have its vertex at the intersection of the
x - axis and the line
x = 4?
ffff ffffA.
fb = 64,
c = 128
B.
fb = - 64,
c = - 64
C.
fb = 64,
c = - 64
D.
fb = - 64,
c = 128
ff
D
Step 1: y = 8x2 + bx + c is a quadratic with a = 8, b = b and c = c.
[Compare with y = ax2 + bx + c.]
Step 2: The intersection of the x - axis and the line x = 4 is the point (4, 0). So the vertex of the given function is at (4, 0).
Step 3: The x - coordinate of the vertex of a quadratic function is given by:
x = - b2a[Substitute the values.]
Step 4: - b2a = 4[Vertex = (4, 0).]
Step 5: b = - 8a[Simplify.]
Step 6: Therefore, b = - 64 [Substitute the values.]
Step 7: Substitute the vertex (4, 0) and b = - 64 in the given equation:
y = 8x2 + bx + c.
Step 8: 0 = 128 - 256 + c[Simplify.]
Step 9: c = 128[Simplify.]