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Solution of deriving vertex from the quadratic function?

2 AND 9


What is the vertex of f(x)2x2 plus 16x plus 9?

To find the vertex of the quadratic function ( f(x) = 2x^2 + 16x + 9 ), we can use the vertex formula. The x-coordinate of the vertex is given by ( x = -\frac{b}{2a} ), where ( a = 2 ) and ( b = 16 ). Thus, ( x = -\frac{16}{2 \cdot 2} = -4 ). Substituting ( x = -4 ) back into the function gives ( f(-4) = 2(-4)^2 + 16(-4) + 9 = 2(16) - 64 + 9 = -64 + 9 + 32 = -23 ). Therefore, the vertex is at the point ( (-4, -23) ).


Which statement describes the rate of change of the following function?

Which statement describes the rate of change of the following function?f(x) = -6x - 9


If you shift the absolute value parent function F(x) x right 9 units what is the equation of the new function?

To shift the absolute value parent function ( F(x) = |x| ) right by 9 units, you replace ( x ) with ( x - 9 ). Therefore, the equation of the new function becomes ( F(x) = |x - 9| ). This transformation moves the vertex of the absolute value function from the origin to the point (9, 0).


What is the vertex of x2 plus 18x plus 19?

The vertex is (-9, -62).


What is the trinomial of x2 plus 8x-9?

x2 + 8x - 9 is a quadratic expression that describes a parabolic function. It can be factored out as: (x + 9)(x - 1) Which tells us that if we graphed it as a function of x, it would intersect the x-axis at the points (-9, 0) and (1, 0). It's derivative is: 2x + 8 which tells us that it's vertex is at the x-location -4, at the point (-4, -25). The second derivative is 2, which tells us that the vertex is a minimum, and that the function's range is: {f(x) | f(x) ≥ -25, f(x) ∈ ℜ}


How do u find the equation of the axis of symmetry and the vertex of the graph of each function for example y x2-8x-9 Plz help i need to know this?

To find the equation of the axis of symmetry for the quadratic function (y = x^2 - 8x - 9), use the formula (x = -\frac{b}{2a}), where (a = 1) and (b = -8). This gives (x = -\frac{-8}{2 \cdot 1} = 4). The vertex can be found by substituting this (x) value back into the original equation: (y = 4^2 - 8(4) - 9 = 16 - 32 - 9 = -25). Thus, the vertex is at the point ((4, -25)) and the axis of symmetry is the line (x = 4).


What is the vertex of the graph of the function below y x2 plus 6x plus 5?

To find the vertex of the quadratic function ( y = x^2 + 6x + 5 ), we can use the vertex formula ( x = -\frac{b}{2a} ). Here, ( a = 1 ) and ( b = 6 ), so ( x = -\frac{6}{2 \cdot 1} = -3 ). To find the ( y )-coordinate, substitute ( x = -3 ) into the equation: ( y = (-3)^2 + 6(-3) + 5 = 9 - 18 + 5 = -4 ). Therefore, the vertex is at the point ((-3, -4)).


What is x2-9?

The expression ( x^2 - 9 ) is a difference of squares, which can be factored as ( (x - 3)(x + 3) ). This means that the expression equals zero when ( x ) is either 3 or -3. The graph of this quadratic function opens upwards and has its vertex at the point (0, -9).


How many diagonals does a hexagon have?

A hexagon has 9 diagonals. Each vertex of a n-sided polygon can be connected to n - 3 others with diagonals. Thus n(n - 3) possible diagonals. However, when Vertex A is connected to vertex C, vertex C is also connected to vertex A, thus each diagonal is counted twice. Thus: number_of_diagonals = n(n - 3)/2 = 6(6-3)/2 = 6x3/2 = 9


How many vertex does a rhomboid have?

9 or 6 depending on what kind of mood its in


What 3d shape has 6 vertex and 9 edges?

A triangular prism.