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Try It 9.125: Determining a Quadratic Function from its Graph
To find a quadratic function from its graph, identify the vertex and another point to substitute into the vertex form, . For example, consider an upward-facing parabola with a vertex at and a -intercept at . The vertex provides and , yielding the partial equation . To find the coefficient , substitute the coordinates of the -intercept for and : . Solving this equation gives , which simplifies to , so . Therefore, the specific quadratic function for this graph is .
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Ch.9 Quadratic Equations and Functions - Intermediate Algebra @ OpenStax
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A small business owner is using a quadratic equation to model the cost of producing items at their workshop. To visualize the cost trends, they need to graph the parabola. Arrange the following steps in the correct standard order for graphing a quadratic equation in two variables.
A financial analyst is graphing a company's profit model, which is represented by a quadratic equation. To ensure the graph is plotted correctly, the analyst follows a standard 7-step procedure. Match each specific graphing task with its correct step number in that procedure.
A financial planner is using the systematic 7-step procedure to graph a quadratic equation representing a client's projected investment growth over time. The planner has already written the equation with 'y' on one side, determined the direction the parabola opens, and found the axis of symmetry and the vertex. According to the procedure, what is the next step the planner should take?
A small business owner is following a systematic 7-step procedure to graph a quadratic equation that models their monthly production costs. True or False: According to this procedure, the very first step the owner should take is to determine whether the parabola opens upward or downward.
Graphing the Final Parabola
Standardized Graphing Procedures
A business analyst is following a systematic 7-step procedure to graph a quadratic equation representing a company's profit trends. According to the fifth step of this procedure, after finding the y-intercept, the analyst must identify the point ________ to the y-intercept across the axis of symmetry.
Production Cost Analysis
A research analyst is following a systematic 7-step procedure to graph a quadratic equation that models a company's market share over time. After completing the first six steps, the analyst prepares for the final step of the process. According to the procedure, which combination of features must be plotted on the graph before drawing the final smooth curve?
A warehouse manager is following a systematic 7-step procedure to graph a quadratic equation that models monthly storage costs. The manager has just completed Step 5 by finding the y-intercept and identifying its symmetric point across the axis of symmetry. According to this procedure, what is the next specific task the manager should perform in Step 6?
Example: Graphing
Example: Graphing
Example 9.61: Graphing
Determining a Quadratic Function from its Graph
Try It 9.125: Determining a Quadratic Function from its Graph
Try It 9.126: Determining a Quadratic Function from its Graph
Graphing a Horizontal Parabola Using Properties
Learn After
A graphic designer is creating a company logo that features a parabolic arch. The designer has identified the vertex of the arch at on a coordinate grid and has correctly substituted these values into the vertex form to obtain the partial equation .
To complete the quadratic function by finding the value of the coefficient , which of the following is the next required step in the standard procedure?
A technical designer is modeling a parabolic arch for a commercial building's entrance. To find the exact mathematical function that represents the arch, the designer must follow a standard procedure using the vertex form . Arrange the following steps in the correct order to determine the quadratic function from its graph.
A technical designer is using the vertex form of a quadratic function, , to model the shape of a parabolic support beam for a new warehouse. True or False: Once the designer has identified and substituted the coordinates of the vertex into the equation, the specific value of the lead coefficient can be determined without requiring any other points from the graph.
A design engineer is using a coordinate system to model the parabolic shape of a suspension cable on a bridge blueprint. To determine the specific equation from the graph, the engineer utilizes the vertex form method. Match each mathematical component to its specific role in this modeling procedure.
A manufacturing quality inspector is analyzing the cross-section of a new parabolic headlight reflector. To determine the specific equation for the reflector's shape using the formula , the inspector first identifies the coordinates of the reflector's lowest central point. In this quadratic formula, this central point is mathematically referred to as the ____.