QuestionApril 19, 2025

Vrite an equation for a parabola with Vertex (-7,1) opens up or down and contains (-4,-26)

Vrite an equation for a parabola with Vertex (-7,1) opens up or down and contains (-4,-26)
Vrite an equation for a parabola with Vertex (-7,1) opens up or down and contains (-4,-26)

Solution
4.7(276 votes)

Answer

y = -3(x + 7)^2 + 1 Explanation 1. Use Vertex Form of Parabola The vertex form is y = a(x - h)^2 + k, where (h, k) is the vertex. Here, h = -7 and k = 1. So, y = a(x + 7)^2 + 1. 2. Substitute Point to Find 'a' Substitute (-4, -26) into the equation: -26 = a(-4 + 7)^2 + 1. Simplify to find a: -26 = a(3)^2 + 1. 3. Solve for 'a' -26 = 9a + 1 \Rightarrow 9a = -27 \Rightarrow a = -3. 4. Write Final Equation Substitute a = -3 back into the vertex form: y = -3(x + 7)^2 + 1.

Explanation

1. Use Vertex Form of Parabola<br /> The vertex form is $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex. Here, $h = -7$ and $k = 1$. So, $y = a(x + 7)^2 + 1$.<br /><br />2. Substitute Point to Find 'a'<br /> Substitute $(-4, -26)$ into the equation: $-26 = a(-4 + 7)^2 + 1$. Simplify to find $a$: $-26 = a(3)^2 + 1$.<br /><br />3. Solve for 'a'<br /> $-26 = 9a + 1 \Rightarrow 9a = -27 \Rightarrow a = -3$.<br /><br />4. Write Final Equation<br /> Substitute $a = -3$ back into the vertex form: $y = -3(x + 7)^2 + 1$.
Click to rate:

Similar Questions