Graphing Quadratics

Front

What is the y-intercept?

Back

The y-intercept is the point where the graph of a function intersects the y-axis. For the equation y = 2x^2 + 8x + 3, the y-intercept is (0,3).

Front

What is the axis of symmetry?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror images. For the quadratic equation y = -x^2 + 4x - 1, the axis of symmetry is x = 2.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola. For the function f(x) = -5(x-2)^2 + 4, the vertex is (2,4).

Front

How do you find the coordinate point for a given x value?

Back

To find the coordinate point, substitute the x value into the function. For f(x) = x^2 - 1, if x = 1, then f(1) = 0, so the coordinate point is (1,0).

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

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

Back

The 'a' value determines the direction of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the formula to find the vertex of a parabola in standard form?

Back

The vertex (h,k) can be found using the formula h = -b/(2a) and k = f(h).

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots. If it's positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

How do you determine the direction of a parabola?

Back

The direction of a parabola is determined by the sign of the 'a' coefficient in the quadratic equation. Positive 'a' means it opens up, negative 'a' means it opens down.

Front

What is the factored form of a quadratic equation?

Back

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