Write the standard form of the equation of the parabola that has the indicated vertex and whose

step 1 This is a question about quadratic functions and models. The question asks us to find the equati

Write the standard form of the equation of the parabola that...

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Key Concepts

Vertex Form of a Parabola

The vertex form of a parabola is an expression of a quadratic function in the form y = a(x - h)² + k, where (h, k) represents the vertex of the parabola. This form makes it easy to identify the vertex and understand the transformation applied to the basic parabola y = x².

Determining the Coefficient Using a Given Point

When a parabola passes through a specific point in addition to having a known vertex, the given point can be substituted into the vertex form equation to solve for the coefficient 'a'. This process involves replacing x and y with the coordinates of the point and then solving the resulting equation.

Standard Form of a Quadratic Equation

The standard form of a quadratic equation is typically written as y = ax² + bx + c. Although the vertex form is useful when the vertex is known, the quadratic can be expanded from vertex form to this standard form, which reveals the coefficients of the quadratic term, linear term, and the constant term.

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