Math Problem Statement
Can you solve this by using Algebraic method not -b/2a
Solution
Certainly! We can solve for and using the given conditions without directly using the formula .
Given Conditions
- The axis of symmetry is .
- The y-intercept is .
The function is .
Step-by-Step Solution
Condition 1: Axis of Symmetry The axis of symmetry is . For the quadratic function , this means that the vertex of the parabola lies on the line .
The x-coordinate of the vertex of a parabola is given by . Here, the vertex lies on . We can use this condition to find :
For :
Condition 2: Y-Intercept The y-intercept occurs when . At this point, the value of is given as . Substituting into the equation:
Since the y-intercept is :
Summary
(a) The values of and are:
Finding the Maximum Value To find the maximum value, we substitute (the axis of symmetry) into the function :
(b) The maximum value of the function is:
Would you like more details or have any questions about this solution? Here are five more questions you might be interested in:
- How do you find the roots of a quadratic function?
- What is the significance of the discriminant in a quadratic equation?
- How do you complete the square to rewrite a quadratic function?
- Can you explain the vertex form of a quadratic function?
- How do you solve a system of equations involving a quadratic and a linear equation?
Tip: Understanding the vertex and intercepts of a quadratic function can help in sketching the graph and solving related problems more effectively.
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Math Problem Analysis
Mathematical Concepts
Quadratic Equations
Vertex of a Parabola
Axis of Symmetry
Formulas
Vertex formula for a quadratic function
Theorems
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Suitable Grade Level
High School