Math Problem Statement
Turn into standerd form
Solution
The graph you provided shows a parabolic function , and we want to express this in standard form. The parabola has the following important points:
- The vertex is at .
- Another point on the parabola is .
General Standard Form of a Quadratic Equation:
The standard form of a quadratic function is: Where is the vertex, and is a constant that determines the direction and width of the parabola.
Step 1: Substitute the vertex
Given that the vertex is , we have:
Step 2: Use the point to find
Substitute and into the equation to solve for :
Step 3: Write the equation
Now that we know , the equation of the parabola in vertex form is:
Step 4: Expand to Standard Form
To convert this into standard form , expand the equation:
Thus, the standard form of the quadratic equation is:
Would you like more details on any part of this process?
Related Questions:
- How can you find the axis of symmetry from a quadratic function in standard form?
- How would you determine the roots of this quadratic function?
- Can you describe how the value of affects the shape of the parabola?
- How would the graph change if the vertex were shifted?
- How can you convert a standard form quadratic function back into vertex form?
Tip:
When finding the equation of a parabola, identifying the vertex and one additional point can help you quickly determine the equation.
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Math Problem Analysis
Mathematical Concepts
Quadratic Equations
Parabolas
Vertex Form
Formulas
f(x) = a(x - h)^2 + k
f(x) = ax^2 + bx + c
Theorems
Quadratic function
Vertex form conversion
Suitable Grade Level
Grades 9-12
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