# Quadratic equations, discriminant, and graph

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative.

Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx + c.

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#### Solution Preview

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative.

Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx + c.

(1) Discriminant is positive

b2 - 4ac > 0

The discriminant is positive for a = 1, b = 3, and c = 1 (32 - 4*1*1 = 9 - 4 = 5 > 0). The equation would be:

y = x2 + ...