Interpreting Quadratic Graphs

Front

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

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation in the form ax^2 + bx + c.

Front

What are the X-intercept(s) of a quadratic graph?

Back

The X-intercepts are the points where the graph crosses the X-axis, found by solving the equation ax^2 + bx + c = 0.

Front

Does a quadratic graph have a maximum or minimum value?

Back

A quadratic graph has a minimum value if it opens upwards (a > 0) and a maximum value if it opens downwards (a < 0).

Front

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

Back

The y-intercept is found by evaluating the function at x = 0, which gives the point (0, c) where c is the constant term in the quadratic equation.

Front

What is the vertex of a quadratic graph?

Back

The vertex is the highest or lowest point on the graph, located at the coordinates (h, k) where h = -b/(2a) and k is the value of the function at x = h.

Front

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

Back

The discriminant, given by the formula D = b^2 - 4ac, determines the nature of the roots of the quadratic equation. 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

The direction of the parabola is determined by the coefficient 'a' in the quadratic equation y = ax^2 + bx + c. If a > 0, it opens upwards; if a < 0, it opens downwards.

Front

What is the significance of the vertex in relation to the axis of symmetry?

Back

The vertex lies on the axis of symmetry, which divides the parabola into two mirror-image halves.

Front

How do you find the coordinates of the vertex from the standard form of a quadratic equation?

Back

For a quadratic in standard form y = ax^2 + bx + c, the vertex coordinates can be found using h = -b/(2a) and k = f(h).

Front

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

Back

The roots of a quadratic equation ax^2 + bx + c = 0 correspond to the values of x that make the equation equal to zero, and can be expressed as factors: a(x - r1)(x - r2) where r1 and r2 are the roots.