Question

The function f(x) = –3x2 + 36x – 119 written in vertex form is f(x) = –3(x – 6)2 – 11. Which statements are true about the graph of f(x)? Select three options.
The axis of symmetry is the line x = 6.
The vertex of the graph is at (–6, –11).
The parabola has a minimum.
The parabola opens down.
The value of h, when the equation is written in vertex form, is positive.

Answer 1

he axis of symmetry is the line x = 6.

The vertex of the graph is at (–6, –11).

The parabola has a minimum.

The parabola opens down.

The value of h, when the equation is written in vertex form, is positive.

Answer 2

Answer:

The symmetric axis is the line $x=6$, the parabola open down and the value of $h$ is positive when written in vertex form are the three true statements.

Step-by-step explanation:

Consider the function as follows:

$f(x)=-3x^2+36x-119$

In vertex form, $f(x)=-3(x-6)^2-11$ ...... (1)

Consider the general vertex form,

$f(x)=a(x-h)^2+k$ ...... (2)

where $(h,k)$ is the vertex of the parabola.

On comparing (1) and (2),

$(h,k)=(6,-11)$ is the vertex of the parabola.

(a) Cleary from the graph, the parabola is symmetric at the line $x=6$.

Thus, the axis of symmetry is the line $x=6$ is true statement.

(b) Since $(6,-11)$ is the vertex of the parabola. Thus, the vertex of the graph is at $(-6,-11)$ is false statement.

(c) The parabola has no minimum as parabola is moving in negative $y$ direction. Thus, parabola has minimum is false statement.

(d) Clearly, from the graph shown, parabola opens downwards is true statement.

(e) In vertex form, value of $h$ is $6$, which is positive is true statement.

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