Mathematics, 04.02.2020 13:01 KennyMckormic

The axis of symmetry for a function in the form f(x) = x2 + 4x − 5 is x = −2. what are the coordinates of the vertex of the graph?

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Answer from: bekahmalcom19

The coordinates of the vertex of the graph are (-2, -9).

Further explanation

The quadratic function is described by the standard equation $\boxed{ \ f(x) = ax^2 + bx + c \ }.$ The graph of a quadratic function is called a parabola.

We have the quadratic function $\boxed{ \ f(x) = x^2 + 4x - 5 \ }.$

We identify the coefficients a, b, and c. For this equation, $\boxed{ \ a = 1, b = 4, and \ c = -5 \ }$ The axis of symmetry is $\boxed{ \ x = h = -\frac{b}{2a} \ }$ , i.e., $\boxed{ \ x = h = -\frac{4}{2(1)} \rightarrow h = -2 \ }.$ Thus, the statement in the question for the symmetry axis x = -2 is correct.The vertex (or turning point) is $\boxed{ \ (h, k) \ },$ where $\boxed{ \ k = f(h) \ }$ or $\boxed{ \ k = \frac{b^2 - 4ac}{-4a} \ }$ The parabola opens upward because a > 0, resulting in a vertex that is a minimum.

Finding the minimum value is as follows:

$\boxed{ \ k = f (-2) = (-2)^2 + 4(-2) - 5 \rightarrow k = -9 \ }, or$ $\boxed{ \ k = \frac{4^2 - 4(1)(-5)}{-4(1)} = -\frac{36}{4} \rightarrow k = -9 \ }$

Therefore, the coordinates of the vertex of the graph are (h, k), i.e., $\boxed{\boxed{ \ (-2, -9) \ }}$

Other components:

The y-intercept of the quadratic function f(x) = x² + 4x - 5 is (0, c), i.e., the point $\boxed{ \ (0, -5) \ }.$ The factorization of f (x) = x² + 4x - 5 becomes f(x) = (x + 5)(x - 1). Then we get the x-intercepts at $\boxed{ \ (-5, 0) \ and \ (1, 0) \ }$ Learn moreWhich is the graph of f(x) = (x - 1)(x + 4) link Finding the y-intercept of the quadratic function f(x) = (x – 6)(x – 2) linkThe midpoint link

Keywords: the axis of symmetry, for a function, f(x) = x² + 4x − 5, x = −2, which is the graph of f(x) = (x - 1)(x + 4), what, the coordinates of the vertex of the graph, the x-intercept, quadratic function, a standard equation, the y-intercept, parabola, upward, the minimum value

The axis of symmetry for a function in the form f(x) = x2 + 4x − 5 is x = −2. what are the coordinat

Answer from: Quest

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

Answer from: Quest

There would be 36.35 pounds