Question

The line of symmetry for the quadratic equation y = ax2 - 2x - 3 is x = 1. What is the value of "a"?

Answer 1

Y = a(x - h)² + k • (h, k) is the vertex • x = h is line of symmetry so y = ax² - 2x - 3 y/a = x² - 2/ax - 3/a y/a + 3/a = x² - 2/ax y/a + 4/a= x² - 2/ax + (-1/a)² ← completing the square y/a + 4/a= (x - 1/a)² y/a = (x - 1/a)² - 4/a y = a(x - 1/a)² - 4 so since you've been given h = 1 then 1/a = 1 and so a = 1 

Answer 2

Answer:

value of a is 1.

Step-by-step explanation:

A quadratic equation $y=ax^2+bx+c$  ....[1]  where a, b and c are the coefficient.

then the axis of symmetry is given by:

$x = -\frac{b}{2a}$             .....[2]

As per the statement:

The line of symmetry for the quadratic equation $y = ax^2-2x -3$  is x = 1.

On comparing given quadratic equation with [1] we have;

b = -2

then;

Substitute x = 1 in [2] we have;

$1= -\frac{-2}{2a}$

Simplify:

$1 = \frac{1}{a}$

⇒$a = 1$

Therefore, the value of a is 1.