1 y=x^2-2 x-8 2 y=2 x^2-3 x 3 y=x^2-4 x+7 4 y=-x^2+2 x+8 5 y=-2 x^2-5 x-2 6 y=x^2+3 x

Let's analyze each equation to understand the type of graph they represent:<br /><br />1. \( y = x^2 - 2x - 8 \)<br /> - This is a quadratic equation in the form \( y = ax^2 + bx + c \) with \( a = 1 \), \( b = -2 \), and \( c = -8 \).<br /> - The graph is a parabola opening upwards.<br /><br />2. \( y = 2x^2 - 3x \)<br /> - This is a quadratic equation in the form \( y = ax^2 + bx + c \) with \( a = 2 \), \( b = -3 \), and \( c = 0 \).<br /> - The graph is a parabola opening upwards.<br /><br />3. \( y = x^2 - 4x + 7 \)<br /> - This is a quadratic equation in the form \( y = ax^2 + bx + c \) with \( a = 1 \), \( b = -4 \), and \( c = 7 \).<br /> - The graph is a parabola opening upwards.<br /><br />4. \( y = -x^2 + 2x + 8 \)<br /> - This is a quadratic equation in the form \( y = ax^2 + bx + c \) with \( a = -1 \), \( b = 2 \), and \( c = 8 \).<br /> - The graph is a parabola opening downwards.<br /><br />5. \( y = -2x^2 - 5x - 2 \)<br /> - This is a quadratic equation in the form \( y = ax^2 + bx + c \) with \( a = -2 \), \( b = -5 \), and \( c = -2 \).<br /> - The graph is a parabola opening downwards.<br /><br />6. \( y = x^2 + 3x \)<br /> - This is a quadratic equation in the form \( y = ax^2 + bx + c \) with \( a = 1 \), \( b = 3 \), and \( c = 0 \).<br /> - The graph is a parabola opening upwards.<br /><br />In summary, the first, second, third, and sixth equations represent parabolas opening upwards, while the fourth and fifth equations represent parabolas opening downwards.