Intro to Quadratics

Front

What is the equation for the axis of symmetry in a quadratic function?

Back

The axis of symmetry is given by the equation x = -b/(2a), where a and b are coefficients from the quadratic equation in the form ax^2 + bx + c.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, found at the coordinates (h, k) in the vertex form of the equation y = a(x-h)^2 + k.

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form ax^2 + bx + c.

Front

What does the 'a' value in a quadratic equation indicate?

Back

The 'a' value determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b^2 - 4ac) determines the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What is the formula to find the roots of a quadratic equation?

Back

The roots can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How can you determine if a quadratic function is a maximum or minimum?

Back

If 'a' is positive, the vertex is a minimum point; if 'a' is negative, the vertex is a maximum point.

Front

What is the axis of symmetry for the quadratic function y = 2x^2 - 4x + 1?

Back

The axis of symmetry is x = -(-4)/(2*2) = 1.