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.

Tags

CCSS.HSA-REI.B.4B

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).

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.