Find the a value of a parabola that has a vertex at (-3,-4) and the point (-6,-25/4) that lies on the curve.

Identify Vertex Form: Identify the vertex form of a parabola. Vertex form: y = a(x-h)^2 + kPlug in Vertex: Plug in the vertex (-3,-4) into the vertex form. y = a(x+3)^2 - 4Substitute Point for 'a': Substitute the point (-6,-25/4) into the equation to find 'a'. -25/4 = a(-6+3)^2 - 4Simplify Equation: Simplify the equation. -25/4 = a(-3)^2 - 4 -25/4 = 9a - 4Move Terms: Move -4 to the left side of the equation. -25/4 + 4 = 9a -25/4 + 16/4 = 9aCombine Fractions: Combine the fractions on the left side. (-25 + 16)/4 = 9a -9/4 = 9aDivide to Solve for 'a': Divide both sides by 9 to solve for 'a'. -9/4 ÷ 9 = a -9/4 * 1/9 = aMultiply Fractions: Multiply the fractions to find 'a'. a = -9/36 a = -1/4

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Find the $a$ value of a parabola that has a vertex at $(-3,-4)$ and the point $(-6,-\frac{25}{4})$ that lies on the curve.

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Algebra 2

Write equations of parabolas in vertex form using properties

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Q. Find the

a

value of a parabola that has a vertex at

(-3,-4)

and the point

(-6,-\frac{25}{4})

that lies on the curve.

Identify Vertex Form: Identify the vertex form of a parabola. $\newline$ Vertex form: $y = a(x-h)^2 + k$
Plug in Vertex: Plug in the vertex $(-3,-4)$ into the vertex form. $\newline$ $y = a(x+3)^2 - 4$
Substitute Point for 'a': Substitute the point $(-6,-\frac{25}{4})$ into the equation to find 'a'. $\newline$ $-\frac{25}{4} = a(-6+3)^2 - 4$
Simplify Equation: Simplify the equation. $\newline$ $-\frac{25}{4} = a(-3)^2 - 4$ $\newline$ $-\frac{25}{4} = 9a - 4$
Move Terms: Move $-4$ to the left side of the equation. $\newline$ $-\frac{25}{4} + 4 = 9a$ $\newline$ $-\frac{25}{4} + \frac{16}{4} = 9a$
Combine Fractions: Combine the fractions on the left side. $\newline$ $(-25 + 16)/4 = 9a$ $\newline$ $-9/4 = 9a$
Divide to Solve for 'a': Divide both sides by $9$ to solve for 'a'. $\newline$ $-\frac{9}{4} \div 9 = a$ $\newline$ $-\frac{9}{4} \times \frac{1}{9} = a$
Multiply Fractions: Multiply the fractions to find $a$ . $a = \frac{-9}{36}$ $a = \frac{-1}{4}$