Vertex Form

Algebra 1 · Axiom Academy

LESSON Vertex Form of Quadratics Written as y = a(x-h)^2 + k , a parabola hands you its turning point for free — and shows you which way it opens. A quadratic can be written in vertex form . The two boxed numbers h and k are the coordinates of the parabola's turning point — no work required. With the vertex pinned at the origin, watch only a change. Its size sets the width and its sign sets the direction — the turning point never moves. The vertex is the lowest point; the arms rise. The parabola flips; the vertex becomes the highest point. Larger |a| stretches the curve vertically, pinching it inward. A fraction flattens the curve, spreading the arms apart. 3. How h and k Move the Vertex Start from y = x^2 (vertex at the origin). Changing h slides the whole parabola horizontally ; changing k slides it vertically . The shape never changes — only where the vertex sits. The vertex moves to x = h . The graph slides h units sideways. The vertex moves to y = k . The graph slides k units up or down. This is where vertex form pays off. To graph y = 2(x - 1)^2 - 3 : plot the vertex, use the sign of a for direction, then grab a couple of symmetric points and sketch. 5. From Standard Form to Vertex Form If a quadratic arrives in standard form y = ax^2 + bx + c , you reach vertex form by completing the square . The animation shows the geometric idea: the missing corner you add (and subtract) makes a perfect square. Reading the y -intercept (0, c)

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