Match each equation in Exercises 17–22 with its graph in choices A–F. y=-(1)/(2) x^2-x+1

Name: Problem 19, Chapter 9: Intermediate Algebra
Uploaded: 2020-07-31T15:36:35-08:00
Duration: 2 min 15 s
Channel: Jacquelyn Trost
Description: Match each equation in Exercises 17–22 with its graph in choices A–F. y=-(1)/(2) x^2-x+1

step 1 Let's take a look at the parabola, y equals negative 1 half x squared minus x plus 1. If we look

Match each equation in Exercises 17–22 with its graph in...

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Key Concepts

Quadratic Functions

A quadratic function is a polynomial function of degree two, typically expressed in the form y = ax² + bx + c. Its graph is a parabola that can open upward (if a > 0) or downward (if a < 0), and understanding its structure is key to analyzing its graph.

Standard Form of a Quadratic Equation

The standard form, y = ax² + bx + c, concisely represents a quadratic equation by clearly displaying its quadratic coefficient (a), linear coefficient (b), and constant term (c). This form is useful for identifying key features of the graph such as the direction of opening and the y-intercept.

Vertex and Axis of Symmetry

The vertex of a quadratic function is the highest or lowest point on the parabola and can be found using the formula x = -b/(2a). This x-value provides the axis of symmetry for the parabola, which is a vertical line that divides the graph into two mirror-image halves. Identifying the vertex aids in graphing the quadratic function accurately.

Direction of Opening

The direction in which a parabola opens is determined by the sign of the coefficient a in the quadratic function. If a is negative, the parabola opens downward, indicating that the vertex is the maximum point. This concept is essential for predicting the general shape of the graph.

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