Identify the y-intercept and the axis of symmetry for the graph of f(x) = 10x^2 + 40x + 42. a 42; x = 4 b 42; x = –2 c –42; x = 2 d 0; x = –4

Question

asked Apr 12, 2021 155k views

2 Answers

Karser · Answer 1 · 2021-04-17T08:44:33+0000

Answer:

The option 'b' is correct.

Explanation:

Given the function

$f\left(x\right)\:=\:10x^2\:+\:40x\:+\:42$

Determining the y-intercept

The y-intercept can be obtained by setting the value x = 0

$y\:=\:10x^2\:+\:40x\:+\:42$

$y\:=\:10\left(0\right)^2\:+\:40\left(0\right)\:+\:42$

= 0+0+42

=42

Therefore, the y-intercept is:

Determining the axis of symmetry

Given the equation

$y=\:10x^2\:+\:40x\:+\:42$

For a parabola in standard form
$y=ax^2\:+\:bx\:+c$

the axis of symmetry is the vertical line that goes through the vertex

x=(-b)/(2a)

so

The axis of symmetry for
$y=ax^2\:+\:bx\:+c$ is
x=(-b)/(2a)

$a=10,\:b=40$

x=(-b)/(2a)

$x=(-40)/(2\cdot \:10)$

x=-2

Therefore, the option 'b' is correct.