Raphael K. answered • 10/14/21
I have mastered Algebra 1 and teach it daily.
Can you please help me?
Factor the quadratic expression in the equation y=2x^2+8x−154 and find the zeros of the equation. Then use the zeros to find the line of symmetry of the parabola represented by the equation.What is the equation for the line of symmetry of the parabola represented by the equation
Hello Bailey,
Set y = 0 before you factor, this will give us the "zeroes" also known as the x-intercepts.
0 = 2x2 + 8x - 154 ..... * Divide everything by 2, since this will simplify things.
0 = x2 + 4x - 77 ........ * Look for the multiples of 77, such as 7 * 11 = 77. So, use 7 and 11 as follows:
0 = (x + 11)(x - 7) ..... * Set each factor equal to 0 and solve.
0 = x + 11
x = -11
0 = x - 7
x = 7
The zeroes or x-intercepts of the parabola are -11, and 7. The axis of symmetry will ALWAYS be exactly in between the two x-intercepts:
Since, there is a gap of 18 units between -11 and 7, you can divide the 18 in half to get the distance from one of the zeroes, to the axis of symmetry, This tells us that the axis of symmetry is 9 units away from the zeroes. So, the axis of symmetry is between the zeroes at either -11 + 9 = -2, or 7 - 9 = -2
Answer:
The axis of symmetry is: x = -2
