Question

what is y= - 2 (x-5) ^ 2 + 3 vertex, axis of symmetry, direction of opening, max or min and y intercept

Answer 1

Answer:

• vertex: (5, 3)
• axis of symmetry: x = 5
• direction of opening: downward
• max: y = 3
• y-intercept: -47

Step-by-step explanation:

Most of the questions can be answered by comparing the given equation to vertex form.

Vertex form

The vertex form of the equation for a parabola is ...

  y = a(x -h)² +k

where 'a' is a vertical scale factor, and (h, k) is the vertex. The sign of 'a' determines whether the parabola opens upward or downward.

Parameter values

When we compare the given equation to the vertex form, we can easily see the values of 'a' and (h, k).

  y = -2(x -5)² +3 . . . . . . . given equation

  y = a(x -h)² +k . . . . . . . vertex form

The parameters are ...

  a = -2, (h, k) = (5, 3)

We notice ...

• the sign of 'a' is negative
• the vertex is (5, 3)

Axis of symmetry

The axis of symmetry is the vertical line through the vertex. It has the equation ...

  x = h

  x = 5 . . . . equation of the axis of symmetry

Direction of opening, max

The sign of 'a' is negative. This means that large x-values will result in large negative y-values. The parabola opens downward.

When the curve opens downward, it means the vertex is the highest point on the curve. The maximum is the y-value of the vertex: k. There is no minimum.

The maximum is y = 3.

Y-intercept

The y-intercept is where the graph crosses the y-axis. It can be found by setting x=0, and computing the value of y:

  y = -2(0 -5)² +3

  y = -2(25) +3 = -50 +3

  y = -47 . . . . the y-intercept.

The ordered pair for the point there is (0, -47).

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We show the graph so you can see how these features relate to the shape of the graph and points on it.