Pregunta
Use the equation \( f(x)=x^{2}+4 x-7 \), to answer parts a) through \( g \) ). a) Determine whether the parabola opens upward or downward. \( x \) The parabola opens dowrward. b) Find the parabola opens upward. The axis of symmetry is \( x=-2 \). (Type an equation.) c) Find the vertex. The vertex of the parabola \( f(x)=x^{2}+4 x-7 \) is (Type an ordered pair.)
Ask by Vargas Ramirez. in the United States
Feb 24,2025
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a) The parabola opens upward.
b) The axis of symmetry is \( x = -2 \).
c) The vertex is (–2, –11).
Solución
We are given f(x) = x² + 4x – 7.
a) Since the coefficient of x² is 1 (which is positive), the parabola opens upward.
b) The axis of symmetry is given by the formula x = –b/(2a). Here, a = 1 and b = 4, so
x = –4/(2 × 1) = –4/2 = –2.
c) The vertex is on the axis of symmetry. To find the y-coordinate, substitute x = –2 into f(x):
f(–2) = (–2)² + 4(–2) – 7
= 4 – 8 – 7
= –11.
Thus, the vertex is (–2, –11).
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Simplifique esta solución Bonus Knowledge
The parabola opens upward because the coefficient of \( x^2 \) is positive. So, you can expect the arms of the parabola to welcome you into its grassy embrace like a friendly hill. The vertex of the parabola \( f(x) = x^2 + 4x - 7 \) can be found by using the formula \( x = -\frac{b}{2a} \). This results in \( x = -2 \). Plugging \( x = -2 \) back into the function, you get \( f(-2) = -11 \), making the vertex \((-2, -11)\). It's like the secret treasure hidden right at the bottom of your parabola!
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