The line of symmetry with a quadratic equation is at the turning point. So find it by putting the equation in turning point form, by using the completing the square method:
2x² - 7x - 15
= x² - (7/2)x - 15/2 halve and square the factor in front of x (not x²), then add and subtract that number to the equation. You now have a factor for a perfect square.
= [x² - (7/2)x + (7/4)²] - (7/4)² - 15/2
= [x² - (7/4)x -(7/4)x + (7/4)²] - 49/16 - 120/16
= (x - 7/4)² - 169/16
the turning point is x = -7/4 and y = - 169/16
To complete the rest of the factorisation using the completing the square method, do this:
(x - 7/4)² ± √(169/16)²
= (x - 7/4)² ± (13/4)²
= (x - 7/4 + 13/4) (x - 7/4 - 13/4)
= (x + 6/4) (x - 20/4)
= (x + 1.5) (x - 5)
Also the question of, "Solve the simultaneous Equations"
The line of symmetry with a quadratic equation is at the turning point. So find it by putting the equation in turning point form, by using the completing the square method:
2x² - 7x - 15
= x² - (7/2)x - 15/2 halve and square the factor in front of x (not x²), then add and subtract that number to the equation. You now have a factor for a perfect square.
= [x² - (7/2)x + (7/4)²] - (7/4)² - 15/2
= [x² - (7/4)x -(7/4)x + (7/4)²] - 49/16 - 120/16
= (x - 7/4)² - 169/16
the turning point is x = -7/4 and y = - 169/16
To complete the rest of the factorisation using the completing the square method, do this:
(x - 7/4)² ± √(169/16)²
= (x - 7/4)² ± (13/4)²
= (x - 7/4 + 13/4) (x - 7/4 - 13/4)
= (x + 6/4) (x - 20/4)
= (x + 1.5) (x - 5)