When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4a

Question

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.

Answer 1

1. b^2-4ac>0 : b>2sqrt(ac)
2. b^2-4ac=0 : b=2sqrt(ac)
3. b^2-4ac<0 : b<2sqrt(ac)

The rest should be a piece of cake.

Answer 2

1+1=2

Answer 3

For firsts, the discriminant is b^2-4*a*c. Now let's look at the three cases.

Positive Discriminant: y = x^2 + 5x + 6
The discriminant is 5^2 - 4*1*6 = 1. This means there are two distinct roots of the equation. In graphing terms, the graph of the equation hits the x-axis twice. Also, because the discriminant is a perfect square, the roots are rational numbers.

Zero Discriminant: y = x^2 - 6x + 9
The discriminat is (-6)^2 - 4*1*9 = 0. This means there is only one root of the equation. When graphed, the equation hits the x-axis only once, at the vertex of the parabola.

Negative Discriminant: y = 2x^2 + x + 7
The discriminant is 1^2 - 4*2*7 = -55. This means there are no real roots of the equation. The graph of this equation does not hit the x-axis at all.

Answer 4

Assuming a>0, when the discriminant is positive, the graph crosses the x-axis twice and the vertex is below the x-axis. A simple equation that does that is y = x²-1.

When the discriminant is 0, the vertex is on the x-axis. y = x²

When the discriminant is negative, the vertex is above the x-axis. y = x²+1

Answer 5

if discriminant is zero... the quadratic equation is a perfect square
Ax2 + Bx + C = 0 ; [ sqrt(A)x + sqrt(C) ]sqrd = 0

if the discriminant is negative.. the roots are imaginary nos.

if the discriminant is positive .. the roots are real nos.

Answer 6

with discriminant negative: x2 + x+5 = 0
graph has no x-intercepts

with discriminant zero: x2 +6x+9=0
graph has one x-intercept

with discriminant postitive: x2 - 4 = 0
graph has 2 x-intercepts

Answer 7

the quadratic equasion is b +or- the Square Root of (b2-4ac) all of this divided by 2a

Answer 8

NO. do your own homework. read the dam book.

Answer 9

Do your homework yourself, honey.

Answer 10

your mom says right
Do UR HOmeWorK AloNe!!!!!!