Graphing Quadratics in Standard Form Review

Front

What is the vertex of a quadratic function in standard form?

Back

The vertex is the highest or lowest point of the parabola, given by the coordinates (h, k) in the vertex form of the equation y = a(x - h)^2 + k.

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

Back

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

Front

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

Back

The 'a' value determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

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 images, given by the equation x = -b/(2a).

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 for upward and negative for downward.

Front

What is the significance of the 'b' value in a quadratic equation?

Back

The 'b' value affects the position of the vertex and the axis of symmetry but does not affect the direction of the parabola.

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

How can you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by solving the equation ax^2 + bx + c = 0 using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation: x = (-b ± √(b^2 - 4ac)) / (2a).