Question

Graph the equation. $$y=x^{2}+2 x-1$$

   Graph the equation.
$$y=x^{2}+2 x-1$$

College Algebra: Graphs and Models

College Algebra: Graphs and Models

Marvin L. Bittinger,… 5th Edition

Chapter 1, Problem 40

Instant Answer

Solved by Expert Ankit Gupta

07/05/2020

Step 1

The given equation \( y = x^2 + 2x - 1 \) is a quadratic equation, which graphs as a parabola. Show more…

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Graph the equation. $$y=x^{2}+2 x-1$$

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Key Concepts

Parabola

A parabola is the shape of the graph of a quadratic function. It is characterized by its symmetric nature, opening upwards or downwards based on the sign of the leading coefficient, and possesses a distinct vertex that represents its maximum or minimum point.

Quadratic Function

A quadratic function is a second-degree polynomial, typically expressed in standard form as ax² + bx + c. Its graph is a curve known as a parabola, and it models a wide range of real-world situations, including trajectories and area problems.

Vertex

The vertex is the highest or lowest point on a parabola and serves as a focal point for graphing quadratic functions. It can be determined by algebraic methods such as completing the square or using the vertex formula derived from the standard form.

Axis of Symmetry

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It passes through the vertex and can be found using the formula x = -b/(2a) from the quadratic function's standard form.

Intercepts

Intercepts are the points where the graph of a function crosses the coordinate axes. For quadratic functions, the y-intercept is found by evaluating the function at x = 0, and the x-intercepts are determined by solving the quadratic equation using methods like factoring, the quadratic formula, or completing the square.

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