Quadratic Equations 4-1

Front

What is the axis of symmetry of the quadratic equation y = 3x² - 6x + 4?

Back

x = 1

Front

How do you find the x-coordinate of the vertex in the equation y = ax² + bx + c?

Back

x = -b/2a

Front

What are the roots of the function f(x) = ½x² + 3x + 7 when graphed?

Back

x = No Real Solutions

Front

Convert the equation y = (x + 8)² + 7 into standard form.

Back

y = x² + 16x + 71

Front

Which of the following is the standard form of a quadratic equation?

Back

y = ax² + bx + c

Front

What is the standard form of a quadratic equation?

Back

y = ax² + bx + c, where a ≠ 0.

Front

What does the vertex of a parabola represent in a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How can you determine if a quadratic equation has real solutions?

Back

By calculating the discriminant (b² - 4ac); if it's positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

Front

What is the formula for the quadratic equation?

Back

x = (-b ± √(b² - 4ac)) / (2a)

Front

What does the term 'discriminant' refer to in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which determines the nature of the roots.