Question

algebra 2a semester online practice
complete this assessment to review what you’ve learned. it will not count
which statement is correct about the quadratic function in vertex form?
$y = 2(x + 8)^2 - 4$
(1 point)
the $y$-intercept is $(0, 128)$.
the axis of symmetry is $x = 8$.
the quadratic function opens downward.
the $y$-intercept is $(0, 124)$.

Explanation:

Step1: Recall Vertex Form Properties

The vertex form of a quadratic function is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex, the axis of symmetry is \( x = h \), and the parabola opens up if \( a > 0 \), down if \( a < 0 \). For \( y = 2(x + 8)^2 - 4 \), rewrite \( x + 8 \) as \( x - (-8) \), so \( h = -8 \), \( k = -4 \), \( a = 2 \).

Step2: Analyze Y-Intercept

To find the y-intercept, set \( x = 0 \):
\( y = 2(0 + 8)^2 - 4 = 2(64) - 4 = 128 - 4 = 124 \). So y-intercept is \((0, 124)\).

Step3: Analyze Axis of Symmetry

Axis of symmetry is \( x = h = -8 \) (since \( h = -8 \) from \( y = 2(x - (-8))^2 - 4 \)), not \( x = 8 \).

Step4: Analyze Direction of Opening

Since \( a = 2 > 0 \), the parabola opens upward, not downward.

Answer:

The y-intercept is \((0, 124)\) (the fourth option: "The y-intercept is \((0, 124)\)")