Question

True or False The graph of $f(x)=2 x^{2}+3 x-4$ opens up.

   True or False The graph of $f(x)=2 x^{2}+3 x-4$ opens up.

College Algebra

College Algebra

Michael Sullivan 10th Edition

Chapter 4, Problem 8

Instant Answer

Solved by Expert Ankit Gupta

05/11/2020

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We want to determine whether the parabola of the function opens upwards or downwards. Show more…

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True or False The graph of $f(x)=2 x^{2}+3 x-4$ opens up.

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Key Concepts

Quadratic Function

A quadratic function is a polynomial function of degree 2, typically expressed in the form ax^2 + bx + c. It is fundamental in algebra and calculus, and its graph is a parabola. Understanding quadratic functions involves analyzing their coefficients and the vertex, axis of symmetry, and roots.

Parabola

A parabola is the graph of a quadratic function. It is a symmetric curve that has a single minimum or maximum point (the vertex). Parabolas are important in many areas of mathematics and physics, providing a model for projectile motion and other phenomena.

Leading Coefficient

The leading coefficient in a quadratic function, which is the coefficient of the x^2 term, determines the direction in which the parabola opens. If the leading coefficient is positive, the parabola opens upward, while if it is negative, the parabola opens downward. This concept is crucial when analyzing the behavior of quadratic functions.

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