SOLUTION: Say whether the graph of the equation y=-x^2+4x-1 opens up, down, left, or right.Give the coordinates of the vertex and the equation of the axis of symmetry.Write your quadratic fu

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Say whether the graph of the equation y=-x^2+4x-1 opens up, down, left, or right.Give the coordinates of the vertex and the equation of the axis of symmetry.Write your quadratic fu      Log On


   

Question 994539: Say whether the graph of the equation y=-x^2+4x-1 opens up, down, left, or right.Give the coordinates of the vertex and the equation of the axis of symmetry.Write your quadratic function in vertex form. Find the maximum or minimum value. Explain how you can determine this value.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Coefficient on leading term is -1. Parabola is concave down. (Opens downward).

Complete the Square to help change to standard form.
y=-%28x%2B2%29%5E2%2B5
Vertex is (-2,5).

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Say whether the graph of the equation y=-x^2+4x-1 opens up, down, left, or right.Give the coordinates of the vertex and the equation of the axis of symmetry.Write your quadratic function in vertex form. Find the maximum or minimum value. Explain how you can determine this value.
y+=+-+x%5E2+%2B+4x+-+1

highlight_green%28y+=+-+%28x+-+2%29%5E2+%2B+3%29 ----- Completed the square to obtain equation in vertex form

Opens concave down since the coefficient on x%5E2 is < 0

Coordinates of the vertex: (2%22%2C%223)

Equation of the axis of symmetry: highlight_green%28x+=+2%29

Maximum value, or y-coordinate of vertex: y+=+-+%282%29%5E2+%2B+4%282%29+-+1, or highlight_green%28y+=+3%29