Review all 3 Forms of Quadratic Graphs

Front

What is the axis of symmetry in a quadratic graph?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a) for a quadratic equation in the form y = ax^2 + bx + c.

Front

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

Back

To find the y-intercept of a quadratic function, substitute x = 0 into the equation and solve for y. The y-intercept is the point (0, y).

Front

What does it mean if a quadratic equation has no real solutions?

Back

If a quadratic equation has no real solutions, it means the graph of the function does not intersect the x-axis. This occurs when the discriminant (b^2 - 4ac) is less than zero.

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 and a ≠ 0.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. It can be found using the formula (h, k) where h = -b/(2a) and k is the value of the function at h.

Front

How do you determine the direction of a parabola?

Back

The direction of a parabola is determined by the coefficient 'a' in the quadratic equation. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is written as y = a(x - r1)(x - r2), where r1 and r2 are the roots (solutions) of the equation.

Front

How can you find the roots of a quadratic equation?

Back

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

Front

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

Back

The discriminant (b^2 - 4ac) indicates the nature of the roots of the quadratic equation. If it is positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Front

What is the y-intercept of the function y = x^2 - 3x - 10?

Back

The y-intercept is (0, -10). This is found by substituting x = 0 into the equation.