Question

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?

Answer 1

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 more

1. Which is the graph of f(x) = (x - 1)(x + 4) brainly.com/question/2334270  
2. Finding the y-intercept of the quadratic function f(x) = (x – 6)(x – 2) brainly.com/question/1332667
3. The midpoint brainly.com/question/3269852  

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

Answer 2

Answer:

-2 -9

Step-by-step explanation: