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parabolas

Solution by Steps

step 1

To find the vertex of the parabola given by the equation

y = ax^2 + bx + c

, we use the vertex formula for a parabola

step 2

The x-coordinate of the vertex is given by

-\frac{b}{2a}

step 3

The y-coordinate of the vertex is given by

c - \frac{b^2}{4a}

step 4

Therefore, the vertex of the parabola is

\left(-\frac{b}{2a}, c - \frac{b^2}{4a}\right)

Answer

The vertex of the parabola

y = ax^2 + bx + c

is

\left(-\frac{b}{2a}, c - \frac{b^2}{4a}\right)

.

Key Concept

Vertex of a Parabola

Explanation

The vertex of a parabola described by

y = ax^2 + bx + c

can be found using the vertex formula, which involves the coefficients of the quadratic equation.

Generate me a similar question

how to calculate the x-coordinate of the vertex of a parabola?

-b/2a

✅Your Answer is correct

Solution by Steps

step 1

The x-coordinate of the vertex of a parabola given by the equation

y = ax^2 + bx + c

can be found using the formula

x = -\frac{b}{2a}

step 2

This formula is derived from completing the square or using calculus to find the axis of symmetry of the parabola, which passes through the vertex

step 3

Apply the formula to the given quadratic equation by identifying the coefficients

a

and

b

and substituting them into the formula

Answer

The x-coordinate of the vertex is

x = -\frac{b}{2a}

.

Key Concept

Vertex of a Parabola

Explanation

The x-coordinate of the vertex of a parabola

y = ax^2 + bx + c

is found using the formula

x = -\frac{b}{2a}

, which represents the axis of symmetry of the parabola.

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