Quadratic Functions in Standard Form Warmup

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c, where a, b, and c are constants.

Front

What does the coefficient 'a' indicate in a quadratic function?

Back

The coefficient 'a' indicates the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

How do you find the vertex of a parabola in standard form?

Back

To find the vertex, use the formula x = -b/(2a) to find the x-coordinate, then substitute this value back into the equation to find the y-coordinate.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0, which gives y = c.

Front

What are the roots or zeroes of a quadratic function?

Back

The roots or zeroes are the x-values where the function equals zero, found by solving the equation ax² + bx + c = 0.

Front

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

Back

The discriminant (D = b² - 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

How can you determine if a quadratic function opens upwards or downwards?

Back

If the coefficient 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the vertex form of a quadratic function?

Back

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

Front

What is the formula for the vertex of a parabola?

Back

The vertex of a parabola can be found using the formula (h, k) where h = -b/(2a) and k is the value of the function at x = h.