Questions: The equation is now in standard form, f(x)=a(x-h)^2+k. Use the equation in standard form to determine the vertex (h, k). Find the axis of symmetry x=h. Finally, determine the exact values of the x-intercepts. The x-intercepts occur where the function is zero. Rewrite the equation, setting the function equal to zero. Solve for x. Write the x-intercepts as ordered pairs.

Solution Steps

To solve the given problem, we need to follow these steps:

1. Identify the vertex \((h, k)\) from the standard form of the quadratic equation \(f(x) = a(x-h)^2 + k\).
2. Determine the axis of symmetry, which is \(x = h\).
3. Find the exact values of the \(x\)-intercepts by setting the function equal to zero and solving for \(x\).

The given quadratic function is in the standard form \( f(x) = a(x-h)^2 + k \). From the given values:

• \( a = 0.4 \)
• \( h = -2 \)
• \( k = -2.4 \)

The vertex \((h, k)\) is: \[ \text{Vertex} = (-2, -2.4) \]

The axis of symmetry for a quadratic function in the form \( f(x) = a(x-h)^2 + k \) is given by \( x = h \). Therefore, the axis of symmetry is: \[ x = -2 \]

To find the \( x \)-intercepts, we set the function equal to zero and solve for \( x \): \[ 0 = 0.4(x + 2)^2 - 2.4 \] Solving this equation, we get: \[ x = -4.4495 \quad \text{and} \quad x = 0.4495 \]

Final Answer