Find the Vertex, Maximum or Minimum, and the Range of f(x) = 1.2x^2 + 3.7x - 5.9

TL;DR

Calculate vertex, maximum/minimum, and range of a quadratic function.

Transcript

hi in this problem we have a quadratic function f of x equals 1.2 x squared plus 3.7 x minus 5.9 and we have to find the vertex the maximum or the minimum and the range so recall that the vertex formula vertex is given by negative b over 2a comma f of negative b over 2a so this is the ordered pair that is the vertex and you might wonder what are th... Read More

Key Insights

• ❓ The vertex of a quadratic function is found using -b/2a.
• 🤘 The direction of the parabola (upwards or downwards) is determined by the sign of 'a'.
• 🤗 Positive 'a' values indicate a parabola opening upwards, leading to a minimum value.
• 🌆 Range of a quadratic function is the set of all possible y-values.

Questions & Answers

Q: How do you find the vertex of a quadratic function?

To find the vertex, calculate -b/2a, where 'a' and 'b' are coefficients in the quadratic equation. This gives the x-coordinate of the vertex. Substitute this back into the function to find the y-coordinate.

Q: What determines whether a quadratic function has a minimum or maximum value?

The sign of the coefficient 'a' in the quadratic function determines if the parabola opens up (minimum) or down (maximum). If 'a' is positive, the function has a minimum value; if negative, it has a maximum.

Q: How is the range of a quadratic function determined?

The range of a quadratic function is all possible y-values it can take. For upward-opening parabolas, the minimum value is the lowest point, and the range extends from this minimum to positive infinity.

Summary & Key Takeaways

• Given a quadratic function, identify the vertex using the formula -b/2a.

• Determine if the parabola opens up or down based on the sign of 'a'.

• Find the minimum or maximum value and range of the function based on the parabola's direction.