Question

The equation y=2(x-1)^2-5y=2(x−1)
2
−5y, equals, 2, left parenthesis, x, minus, 1, right parenthesis, squared, minus, 5 is graphed in the xyxyx, y-plane. Which of the following statements about the graph is true?

Answer 1

Answer:

(b) It is symmetrical about $x = 1$

Step-by-step explanation:

Given

$y = 2(x - 1)^2 - 5$

See attachment for options

Required

True statement about the graph

First, we check the line of symmetric

$y = 2(x - 1)^2 - 5$

Expand

$y = 2(x^2 - 2x + 1) - 5$

Open bracket

$y = 2x^2 - 4x + 2 - 5$

$y = 2x^2 - 4x -3$

A quadratic equation $y = ax^2 + bx + c$ has the following line of symmetry

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

By comparison, the equation becomes:

$x = -\frac{-4}{2*2}$

$x = \frac{4}{4}$

$x = 1$

Hence, the line of symmetry is at: $x = 1$

(b) is true.

Answer 2

Answer: It is symmetrical about x=1

Step-by-step explanation: