Answer:
The correct option is C). 42,x=(-2)
Point (0,42) is y-intercept of f(x)
x+2=0 is equation of axis of symmetry
Step-by-step explanation:
The given function is f(x)=[tex]10x^{2} +40x+42[/tex]
To find y-intercept:
The y-intercept is point were x=0
y=f(x)=[tex]10x^{2} +40x+42[/tex]
y=f(0)=[tex]10(0)^{2} +40(0)+42[/tex]
y=42
Therefore,Point (0,42) is y-intercept of f(x)
To find axis of symmetry of f(x):
We know that f(x) is equation of parabola
Hence, the x -coordinate of the vertex of the parabola is the equation of the axis of symmetry.
if the equation of parabola is f(x)=[tex]ax^{2} +bx+c[/tex] then, the axis of symmetry is given by x=[tex]-\frac{b}{2a}[/tex]
Therefore, for f(x)=[tex]10x^{2} +40x+42[/tex]
The axis of symmetry will be,
x=[tex]-\frac{b}{2a}[/tex]
a=10 and b=40
x=[tex]-\frac{40}{2(10)}[/tex]
x=-2
x+2=0 is equation of axis of symmetry
Thus,
The correct option is C). 42,x=(-2)
Note: In figure, blue curve is f(x) and black line is axis of symmetry
