Find the quadratic function y=a x^2+c with a graph that has the given points. (-3,89),(2,39)

Name: Problem 51, Chapter 5: Algebra 2
Uploaded: 2020-01-01T02:40:28-08:00
Duration: 2 min 34 s
Channel: Martha Richards
Description: Find the quadratic function y=a x^2+c with a graph that has the given points. (-3,89),(2,39)

step 1 All right, so this problem here asks us to find a quadratic equation here in the form of y equal

Find the quadratic function y=a x^2+c with a graph that has...

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Key Concepts

Quadratic Functions

A quadratic function is a second degree polynomial, typically written in the form y = ax² + bx + c. It describes a parabolic curve on the coordinate plane and is a fundamental concept in algebra, with its graph characterized by features such as the vertex and axis of symmetry.

Formulating a System of Equations Using Known Points

When a quadratic function must pass through specific points, substituting the x and y values of these points into the quadratic equation produces a system of equations. This system can then be solved to determine the unknown coefficients, ensuring that the function satisfies the given conditions.

Techniques for Solving Systems of Equations

Solving a system of equations typically involves methods such as substitution or elimination. These algebraic techniques allow one to isolate and determine the values of the unknown parameters in the function, ensuring a consistent solution that satisfies all given constraints.

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