Answer:
option 4
y = 2x² + 8x + 8
Explanation:
the quadratic equation is the one which always generates a parabola or a curve in the graph so let's check which of the given equations are quadratic,
1
y = 9x² + 6x + 4
quadratic formula, X = -b +- √b² - 4ac / 2a
= -6 +- √6² - 4*9*4 / 2*9
= -6 +- √36-144 / 18
no this is not a quadratic equation
let's check the option 2
y = 6x² - 12x - 6
quadratic formula, x = -(-12) +- √12² - 4*6*-6 / 2(6)
= 12 +- √144+144 / 12
not a perfect square so this also is not a quadratic equation.
let's check option 3,
y = 3x² + 7x + 5
quadratic formula, x = -7 +- √7² - 4*3*5 / 2(3)
= -7 +- √49-60 / 6
invalid square root so again is not a quadratic equation
let's check option 4
y = 2x² + 8x + 8
quadratic formula, x = -8 +- √8² - 4*2*8 / 2(2)
= -8 +- √64-64 /4 = -8/4 = -2
yes this is a quadratic equation and the graph for it will be a curved graph