What is the equation of the graph below?
a graph shows a parabola that opens up and crosses the x axis near one and a half and four and a half.
answers:
y = − (x − 3)2 − 2
y = − (x + 2)2 − 3
y = (x − 3)2 − 2
y = (x + 2)2 − 3

C). y = (x − 3)² − 2

We will solve the problems associated with the quadratic functions.

Given:

A graph shows a parabola that opens up and crosses the x-axis near one and a half and four and a half.

Question:

What is the equation of the graph below?

A) y = − (x − 3)² − 2

B) y = − (x + 2)² − 3

C) y = (x − 3)² − 2

D) y = (x + 2)² − 3

The Process:

If we know the vertex point of the parabola, V(h, k), then we use the formula:

When , the parabola opens upward. Therefore we have C or D as a candidate for the answer.

The axis of symmetry is the line that passes through the vertex of a parabola with equation:

If (x₁, 0) and (x₂,0) are the x-intercepts of the graph, then the axis of symmetry can also be determined by

From the problem, the graph crosses the x-axis near one and a half and four and a half. So we can find the axis of the symmetry.

Thus, we have found the equation of the graph, which is .

From the equation of the graph, we know that the vertex point of the parabola is (h, k) = (3, -2), resulting in a vertex that is a minimum.

See the attachment.

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Notes:

Let us change to standard equation form.

y = (x − 3)² − 2

y = x² - 6x + 9 - 2

y = x² - 6x + 7

A quadratic function is described by the standard equation , and the value c is the y-intercept of the graph.

See the attachment once again, the y-intercept is (0, 7).

Keywords: a graph, shows a parabola, that opens up, crosses the x-axis, near one and a half, four, the quadratic functions, the equation of the graph, vertex, the axis of symmetry, opens upward, the x-intercept, the y-intercept, minimum

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

ome people is not even worth it to even try it in the air.

step-by-step explanation: