Question

A quadratic relation in the form y = ax² + bx + c and has a y-intercept of (0, 1). The parabola also goes through the points (2, 9) and (-5, 16). Determine the parameters of this quadratic relation (the values of a, b, and c).

Answer 1

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A nonlinear function that can be written on the standard form

ax² + bx + c,wherea ≠ 0

is called a quadratic function.

All quadratic functions has a U-shaped graph called a parabola.

The parent quadratic function is

y = x²

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The lowest or the highest point on a parabola is called the vertex. The vertex has the x-coordinate

x= −b/2a

The y-coordinate of the vertex is the maximum or minimum value of the function.

a > 0 parabola opens up minimum value

positive symbol before x2 we get a happy expression on the graph and a negative symbol renders a sad expression.

The vertical line that passes through the vertex and divides the parabola in two is called the axis of symmetry.

The axis of symmetry has the equation

x=−b/2a

The y-intercept of the equation is c.

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