In Exercises 17-34, write the quadratic function in standard form and sketch its graph. Identify

step 1 So for this poem, we're asked to write this quadratic function in standard form, which is alread

In Exercises 17-34, write the quadratic function in standard...

Key Concepts

x-intercepts

The x-intercepts of a quadratic function are the points where the graph crosses the x-axis, which occur when f(x) = 0. These intercepts are found by solving the quadratic equation ax² + bx + c = 0.

Axis of Symmetry

The axis of symmetry is the vertical line that bisects the parabola, dividing it into two congruent halves. Its equation is given by x = -b/(2a) when the quadratic function is written in standard form.

Graph of a Parabola

Graphing a quadratic function involves plotting its parabola by identifying the vertex, the axis of symmetry, and the intercepts. The shape and orientation (upward or downward) are determined by the sign of the coefficient a, and these key features help in accurately sketching the function.

Standard Form

The standard form of a quadratic function is f(x) = ax² + bx + c. This form clearly shows the coefficients of the quadratic term, the linear term, and the constant term, making it straightforward to identify key features like the vertex and intercepts.

Quadratic Function

A quadratic function is a second-degree polynomial function typically expressed in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ? 0. Its graph is a parabola, which opens upward when a is positive and downward when a is negative.

Vertex of a Parabola

The vertex of a parabola is the point where the function attains its maximum value (if the parabola opens downward) or its minimum value (if it opens upward). It can be located using the formula (-b/(2a), f(-b/(2a))) or by completing the square to rewrite the function in vertex form.

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