Math 3 wk 2

Front

What is the discriminant of the quadratic equation ax² + bx + c = 0?

Back

The discriminant is given by the formula D = b² - 4ac. It determines the nature of the roots of the quadratic equation.

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real root (a repeated root).

Front

How do you complete the square for the expression x² - 3x?

Back

To complete the square, take half of the coefficient of x (which is -3), square it (which gives 9/4), and add it to the expression.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of the quadratic equation ax² + bx + c = 0.

Front

What are the steps to solve a quadratic equation using the quadratic formula?

Back

1. Identify a, b, and c from the equation. 2. Calculate the discriminant D = b² - 4ac. 3. Substitute a, b, and D into the quadratic formula.

Front

What is the solution of the equation 3x² + 2x - 5 = 0 using the quadratic formula?

Back

x = ( -2 ± √(2² - 4*3*(-5)) ) / (2*3) = ( -2 ± √64 ) / 6 = ( -2 ± 8 ) / 6, giving x = 1 or x = -5/3.

Front

How do you find the roots of the equation 2x² + 16x + 28 = 0?

Back

Use the quadratic formula: x = (-16 ± √(16² - 4*2*28)) / (2*2). Calculate the discriminant and solve for x.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

Complete the square on the quadratic expression to rewrite it in the form y = a(x - h)² + k.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.