# SOLUTION: 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. (When the discr

Algebra ->  -> SOLUTION: 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. (When the discr      Log On

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 Click here to see ALL problems on Quadratic Equations Question 76249: 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. (When the discriminant is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. ) Explain what the value of the discriminant means to the graph of y = ax2 + bx + c. Hint: Chose values of a, b and c to create a particular discriminant. Then, graph the corresponding equation?Answer by Edwin McCravy(9717)   (Show Source): You can put this solution on YOUR website!``` When using the quadratic formula to solve a quadratic equation , the discriminant is . This discriminant can be positive, zero, or negative. (When the discriminant is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. ) Explain what the value of the discriminant means to the graph of y = ax2 + bx + c. Hint: Chose values of a, b and c to create a particular discriminant. Then, graph the corresponding equation? Choose a = 1, b = 4, c = -21 Then the equation is y = x² + 4x - 21 and the discriminant is (4)² - 4(1)(-21) = 16 + 84 = 100, which is positive. The graph intersects the x-axis twice, once at x = -7 and again at x = 3. There are two real zeros, -7, and 3 ----------------- Now choose a = 1, b = 4, c = 4 Then the equation is y = x² + 4x + 4 and the discriminant is (4)² - 4(1)(4) = 16 - 16 = 0. The graph just touches the x-axis at -2. There is just one real zeros, -2. [This zero is said to have multiplicity 2 because people like to think of the graph as "crossing the x-axis twice at the same point", and "both its two zeros are the same, i.e., 'merging' into one".] ------------------- Finally choose a = 1, b = 4, c = 6 Then the equation is y = x² + 4x + 6 and the discriminant is (4)² - 4(1)(6) = 16 - 24 = -8, which is negative. The graph does not cross or touch the x-axis. Therefore it has no real zeros, which means that both its solutions are imaginary. Edwin```