How Do You Find the Y-Coordinate of a Parabola's Vertex?

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SUMMARY

The discussion focuses on finding the y-coordinate of the vertex of a downward-opening parabola represented by the equation y = -0.0022x² + 1.578x. The x-coordinate of the vertex was correctly calculated using the formula x = -b/2a, resulting in x = 179.31815. To find the corresponding y-coordinate, participants are prompted to substitute this x-value back into the original equation.

PREREQUISITES
  • Understanding of quadratic equations and their standard form
  • Familiarity with the vertex formula x = -b/2a
  • Ability to perform polynomial substitution
  • Basic knowledge of parabolic graphs and their properties
NEXT STEPS
  • Learn how to derive the vertex form of a parabola
  • Study the properties of quadratic functions and their graphs
  • Explore applications of parabolas in real-world scenarios
  • Practice solving for y-coordinates using various quadratic equations
USEFUL FOR

Students studying algebra, particularly those tackling quadratic functions and their applications, as well as educators looking for examples to illustrate vertex calculations.

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Homework Statement

Sorry for such an elementary question, but I'm struggling thru Int Alg. Today's nightmare involves a downward parabola. An arch supporting a bridge has the equation y=-0.0022x^2 + 1.578x + 0. Position of left side parabolic arch is (0,0). Using x = -b/2a, I calculated the symmetrical point of the parabola at (358.6363,0). If this is correct, the vertex x-coordinate is 179.31815. I'm stuck at finding the y coordinate of the vertex. Any help would be greatly appreciated.



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The Attempt at a Solution

 
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You know that y=-0.0022x^2 + 1.578x. What is y when x = 179.31815?
 

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