Mathematics, 24.08.2019 14:30 kylierice1

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

Answers: 2

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Answers

Answer from: mikemurray115

C). y = (x − 3)² − 2

Further explanation

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: $\boxed{\boxed{ \ y = a(x - h)^2 + k \ }}$

When $\boxed{ \ a 0 \ }$ , 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: $\boxed{ \ x = h = - \frac{b}{2a} \ }$

If (x₁, 0) and (x₂,0) are the x-intercepts of the graph, then the axis of symmetry can also be determined by $\boxed{ \ x = h = \frac{x_1 + x_2}{2} \ }$

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.

$\boxed{ \ x = h = \frac{1.5 + 4.5}{2} \ }$

$\boxed{ \ h = 3 \ }$

Thus, we have found the equation of the graph, which is $\boxed{\boxed{ \ C) \ y = (x - 3)^2 - 2 \ }}$ .

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.

- - - - - - - - - -

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 $\boxed{\boxed{ \ f(x) = ax^2 + bx + c \ }}$ , and the value c is the y-intercept of the graph.

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

Learn moreWhat are the coordinates of the vertex of the graph f(x) = x² + 4x − 5? What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? Which is the graph of f(x) = (x - 1)(x + 4)

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

What is the equation of the graph below? a graph shows a parabola that opens up and crosses the x

Answer from: Quest

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Answer from: Quest

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What is the equation of the graph below?
a graph shows a parabola that opens up and crosses...