Question

1. Identify the y-intercept and the axis of symmetry for the graph of

Answer 1

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)=$10x^{2} +40x+42$

To find y-intercept:

The y-intercept is point were x=0

y=f(x)=$10x^{2} +40x+42$

y=f(0)=$10(0)^{2} +40(0)+42$

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)=$ax^{2} +bx+c$ then, the axis of symmetry is given by x=$-\frac{b}{2a}$

Therefore, for f(x)=$10x^{2} +40x+42$

The axis of symmetry will be,

x=$-\frac{b}{2a}$

a=10 and b=40

x=$-\frac{40}{2(10)}$

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