Academic Recovery #2/ Forms of Quadratics

Front

What is the intercepts (factored) form of a quadratic equation?

Back

The intercepts (factored) form of a quadratic equation is expressed as y = a(x - p)(x - q), where p and q are the x-intercepts.

Front

How do you find the maximum height of a projectile modeled by a quadratic equation?

Back

To find the maximum height, use the vertex formula t = -b/(2a) from the standard form h(t) = at^2 + bt + c, where a, b, and c are coefficients.

Front

What does it mean if a quadratic graph has a minimum value?

Back

A quadratic graph has a minimum value if it opens upwards (a > 0), indicating the vertex is the lowest point on the graph.

Front

How do you determine the x-intercepts of a quadratic function?

Back

To find the x-intercepts, set y = 0 and solve the equation for x.

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 significance of the coefficient 'a' in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the graph.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants.

Front

How can you identify the direction of a parabola from its equation?

Back

The direction of a parabola can be identified by the sign of the coefficient 'a': if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the formula to find the axis of symmetry of a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form y = ax^2 + bx + c.

Front

What is the relationship between the roots of a quadratic equation and its graph?

Back

The roots (or x-intercepts) of a quadratic equation are the points where the graph intersects the x-axis.